YALE  UNIVERSITY 
MRS.  HEPSA  ELY  SILLIMAN  MEMORIAL  LECTURES 


ELECTRICITY  AND   MATTER 


.ELECTRICITY  AND 
MATTER 


BY 


J.  J.  THOMSON,  D.Sc.,  LL.D.,  PH.D.,  F.R.S. 

i  « 

FELLOW    OF    TRINITY   COLLEGE,    CAMBRIDGE;    CAVENDISH 
PROFESSOR    OF   EXPERIMENTAL    PHYSICS,    CAMBRIDGE 


WITH   DIAGRAMS 


NEW  YORK 

CHARLES   SCRIBNER'S   SONS 
1904 


COPYRIGHT,  1904 
BY  YALE  UNIVERSITY 

Published,  March,  1904 


TROW  DIRECTORY 

PRINTING  AND  BOOKBINDING   COMPANY 


"TV 


THE   SILLIMAN  FOUNDATION. 

In  the  year  1883  a  legacy  of  eighty  thousand  dollars 
was  left  to  the  President  and  Fellows  of  Yale  College 
in  the  city  of  New  Haven,  to  be  held  in  trust,  as  a 
gift  from  her  children,  in  memory  of  their  beloved  and 
honored  mother  Mrs.  Hepsa  Ely  Silliman. 

On  this  foundation  Yale  College  was  requested  and 
directed  to  establish  an  annual  course  of  lectures  de- 
signed to  illustrate  the  presence  and  providence,  the 
wisdom  and  goodness  of  God,  as  manifested  in  the 
natural  and  moral  world.  These  were  to  be  designated 
as  the  Mrs.  Hepsa  Ely  Silliman  Memorial  Lectures.  It 
was  the  belief  of  the  testator  that  any  orderly  presenta- 
tion of  the  facts  of  nature  or  history  contributed  to 
the  end  of  this  foundation  more  effectively  than  any 
attempt  to  emphasize  the  elements  of  doctrine  or  of 
creed;  and  he  therefore  provided  that  lectures  on  dog- 
matic or  polemical  theology  should  be  excluded  from 
the  scope  of  this  foundation,  and  that  the  subjects  should 
be  selected  rather  from  the  domains  of  natural  science 
and  history,  giving  special  prominence  to  astronomy, 
chemistry,  geology,  and  anatomy. 

It  was  further  directed  that  each  annual  course  should 
be  made  the  basis  of  a  volume  to  form  part  of  a  series 
constituting  a  memorial  to  Mrs.  Silliman.  The  memo- 
rial fund  came  into  the  possession  of  the  Corporation 
of  Yale  University  in  the  year  1902;  and  the  present 
volume  constitutes  the  first  of  the  series  of  memorial 
lectures. 


PREFACE 

In  these  Lectures  given  at  Yale  University  in 
May,  1903,  I  have  attempted  to  discuss  the  bear- 
ing of  the  recent  advances  made  in  Electrical 
Science  on  our  views  of  the  Constitution  of  Matter 
and  the  Nature  of  Electricity;  two  questions 
which  are  probably  so  intimately  connected,  that 
the  solution  of  the  one  would  supply  that  of  the 
other.  A  characteristic  feature  of  recent  Electri- 
cal Researches,  such  as  the  study  and  discovery 
of  Cathode  and  Rontgen  Rays  and  Radio-active 
Substances,  has  been  the  very  especial  degree  in 
which  they  have  involved  the  relation  between 
Matter  and  Electricity. 

In  choosing  a  subject  for  the  Silliman  Lectures, 
it  seemed  to  me  that  a  consideration  of  the  bear- 
ing of  recent  work  on  this  relationship  might  be 
suitable,  especially  as  such  a  discussion  suggests 
multitudes  of  questions  which  would  furnish  ad- 
mirable subjects  for  further  investigation  by  some 
of  my  hearers. 

Cambridge,  Aug.,  1903. 

J.  J.  THOMSON. 


CONTENTS 

CHAPTER'  I 

PAGE 

REPRESENTATION  OF  THE  ELECTRIC  FIELD  BY  LINES 

OF  FORCE 1 

CHAPTER   II 

ELECTRICAL  AND  BOUND  MASS 36 

CHAPTER  III 

EFFECTS  DUE   TO  THE   ACCELERATION   OF   FARADAY 

TUBES 53 

€HAPTER   IV 

THE  ATOMIC  STRUCTURE  OF  ELECTRICITY     .        .        .71 

CHAPTER  V 
THE  CONSTITUTION  OF  THE  ATOM 90 

CHAPTER  VI 

RADIO-ACTIVITY  AND  RADIO-ACTIVE  SUBSTANCES  .        .     140 


I    UNP 


OF  THE 

UNIVERSITY 
\ 

X^, 


ELECTRICITY  AND  MATTER 

CHAPTER  I 

REPRESENTATION  OF  THE  ELECTRIC  FIELD 
BY  LINES  OF  FORCE 

MY  object  in  these  lectures  is  to  put  before  you 
in  as  simple  and  untechnical  a  manner  as  I  can 
some  views  as  to  the  nature  of  electricity,  of  the 
processes  going  on  in  the  electric  field,  and  of  the 
connection  between  electrical  and  ordinary  matter 
which  have  been  suggested  by  the  results  of  recent 
investigations. 

The  progress  of  electrical  science  has  been 
greatly  promoted  by  speculations  as  to  the  nature 
of  electricity.  Indeed,  it  is  hardly  possible  to 
overestimate  the  services  rendered  by  two  theories 
as  old  almost  as  the  science  itself;  I  mean  the 
theories  known  as  the  two-  and  the  one-fluid 
theories  of  electricity. 

The  two-fluid  theory  explains  the  phenomena 
of  electro-statics  by  supposing  that  in  the  universe 
there  are  two  fluids,  uncreatable  and  indestruc- 


2  ELECTRICITY   AND    MATTER 

tible,  whose  presence  gives  rise  to  electrical  effects ; 
one  of  these  fluids  is  called  positive,  the  other 
negative  electricity,  and  electrical  phenomena 
are  explained  by  ascribing  to  the  fluids  the  fol- 
lowing properties.  The  particles  of  the  positive 
fluid  repel  each  other  with  forces  varying  inversely 
as  the  square  of  the  distance  between  them,  as  do 
also  the  particles  of  the  negative  fluid;  on  the 
other  hand,  the  particles  of  the  positive  fluid  at- 
tract those  of  the  negative  fluid.  The  attraction 
between  two  charges,  m  and  m',  of  opposite  signs 
are  in  one  form  of  the  theory  supposed  to  be 
exactly  equal  to  the  repulsion  between  two 
charges,  m  and  m  of  the  same  sign,  placed  in 
the  same  position  as  the  previous  charges.  In  an- 
other development  of  the  theory  the  attraction  is 
supposed  to  slightly  exceed  the  repulsion,  so  as  to 
afford  a  basis  for  the  explanation  of  gravitation. 

The  fluids  are  supposed  to  be  exceedingly  mo- 
bile and  able  to  pass  with  great  ease  through  con- 
ductors. The  state  of  electrification  of  a  body  is 
determined  by  the  difference  between  the  quanti- 
ties of  the  two  electric  fluids  contained  by  it ;  if  it 
contains  more  positive  fluid  than  negative  it  is 
positively  electrified,  if  it  contains  equal  quantities 
it  is  uncharged.  Since  the  fluids  are  uncreatable 


LINES   OF    FORCE  3 

and  indestructible,  the  appearance  of  the  positive 
fluid  in  one  place  must  be  accompanied  by  the 
departure  of  the  same  quantity  from  some  other 
place,  so  that  the  production  of  electrification  of 
one  sign  must  always  be  accompanied  by  the  pro- 
duction of  an  equal  amount  of  electrification  of 
the  opposite  sign. 

On  this  view,  every  body  is  supposed  to  con- 
sist of  three  things :  ordinary  matter,  positive  elec- 
tricity, negative  electricity.  The  two  latter  are 
supposed  to  exert  forces  on  themselves  and  on 
each  other,  but  in  the  earlier  form  of  the  theory 
no  action  was  contemplated  between  ordinary 
matter  and  the  electric  fluids ;  it  was  not  until  a 
comparatively  recent  date  that  Helmholtz  intro- 
duced the  idea  of  a  specific  attraction  between 
ordinary  matter  and  the  electric  fluids.  He  did  this 
to  explain  what  is  known  as  contact  electricity, 
i.e.j  the  electrical  separation  produced  when  two 
metals,  say  zinc  and  copper,  are  put  in  contact 
with  each  other,  the  zinc  becoming  positively,  the 
copper  negatively  electrified.  Helmholtz  sup- 
posed that  there  are  forces  between  ordinary  mat- 
ter and  the  electric  fluids  varying  for  different 
kinds  of  matter,  the  attraction  of  zinc  for  positive 
electricity  being  greater  than  that  of  copper,  so 


4  ELECTRICITY   AND    MATTER 

that  when  these  metals  are  put  in  contact  the 
zinc  robs  the  copper  of  some  of  its  positive 
electricity. 

There  is  an  indefmiteness  about  the  two-fluid 
theory  which  may  be  illustrated  by  the  considera- 
tion of  an  unelectrified  body.  All  that  the  two- 
fluid  theory  tells  us  about  such  a  body  is  that  it 
contains  equal  quantities  of  the  two  fluids.  It  gives 
no  information  about  the  amount  of  either;  indeed, 
it  implies  that  if  equal  quantities  of  the  two  are 
added  to  the  body,  the  body  will  be  unaltered, 
equal  quantities  of  the  two  fluids  exactly  neutraliz- 
ing each  other.  If  we  regard  these  fluids  as  being 
anything  more  substantial  than  the  mathematical 
symbols  +  and  —  this  leads  us  into  difficulties ;  if 
we  regard  them  as  physical  fluids,  for  example,  we 
have  to  suppose  that  the  mixture  of  the  two  fluids 
in  equal  proportions  is  something  so  devoid  of 
physical  properties  that  its  existence  has  never 
been  detected. 

The  other  fluid  theory — the  one-fluid  theory  of 
Benjamin  Franklin— is  not  open  to  this  objection. 
On  this  view  there  is  only  one  electric  fluid,  the 
positive ;  the  part  of  the  other  is  taken  by  ordi- 
nary matter,  the  particles  of  which  are  supposed 
to  repel  each  other  and  attract  the  positive  fluid, 


LINES    OF    FORCE  5 

just  as  the  particles  of  the  negative  fluid  do  on 
the  two-fluid  theory.  Matter  when  unelectrified 
is  supposed  to  be  associated  with  just  so  much  of 
the  electric  fluid  that  the  attraction  of  the  matter 
on  a  portion  of  the  electric  fluid  outside  it  is  just 
sufficient  to  counteract  the  repulsion  exerted  on 
the  same  fluid  by  the  electric  fluid  associated  with 
the  matter.  On  this  view,  if  the  quantity  of  mat- 
ter in  a  body  is  known  the  quantity  of  electric 
fluid  is  at  once  determined. 

The  services  which  the  fluid  theories  have  ren- 
dered to  electricity  are  independent  of  the  notion 
of  a  fluid  with  any  physical  properties ;  the  fluids 
were  mathematical  fictions,  intended  merely  to  give 
a  local  habitation  to  the  attractions  and  repulsions 
existing  between  electrified  bodies,  and  served  as 
the  means  by  which  the  splendid  mathematical 
development  of  the  theory  of  forces  varying  in- 
versely as  the  square  of  the  distance  which  was 
inspired  by  the  discovery  of  gravitation  could  be 
brought  to  bear  on  electrical  phenomena.  As 
long  as  we  confine  ourself  to  questions  which  only 
involve  the  law  of  forces  between  electrified  bodies, 
and  the  simultaneous  production  of  equal  quantities 
of  +  and  —  electricity,  both  theories  must  give 
the  same  results  and  there  can  be  nothing  to 


(J  ELECTRICITY    AND    MATTER 

decide  between  them.  The  physicists  and  mathe- 
maticians who  did  most  to  develop  the  "Fluid 
Theories  "  confined  themselves  to  questions  of  this 
kind,  and  refined  and  idealized  the  conception  of 
these  fluids  until  any  reference  to  their  physical 
properties  was  considered  almost  indelicate.  It  is 
not  until  we  investigate  phenomena  which  involve 
the  physical  properties  of  the  fluid  that  we  can 
hope  to  distinguish  between  the  rival  fluid  the- 
ories. Let  us  take  a  case  which  has  actually 
arisen.  We  have  been  able  to  measure  the  masses 
associated  with  given  charges  of  electricity  in 
gases  at  low  pressures,  and  it  has  been  found  that 
the  mass  associated  with  a  positive  charge  is  im- 
mensely greater  than  that  associated  with  a  nega- 
tive one.  This  difference  is  what  we  should 
expect  on  Franklin's  one-fluid  theory,  if  that 
theory  were  modified  by  making  the  electric  fluid 
correspond  to  negative  instead  of  positive  elec- 
tricity, while  we  have  no  reason  to  anticipate  so 
great  a  difference  on  the  two-fluid  theory.  We 
shall,  I  am  sure,  be  struck  by  the  similarity  be- 
tween some  of  the  views  which  we  are  led  to  take 
by  the  results  of  the  most  recent  researches  with 
those  enunciated  by  Franklin  in  the  very  infancy 
of  the  subject. 


LINES   OF    FORCE  7 

Faradwifs  Line  of  Force  Theoi^y 

The  fluid  theories,  from  their  very  nature,  imply 
the  idea  of  action  at  a  distance.  This  idea,  al- 
though its  convenience  for  mathematical  analysis 
has  made  it  acceptable  to  many  mathematicians,  is 
one  which  many  of  the  greatest  physicists  have 
felt  utterly  unable  to  accept,  and  have  devoted 
much  thought  and  labor  to  replacing  it  by  some- 
thing involving  mechanical  continuity.  Pre-emi- 
nent among  them  is  Faraday.  Faraday  was  deeply 
influenced  by  the  axiom,  or  if  you  prefer  it,  dogma 
that  matter  cannot  act  where  it  is  not.  Faraday, 
who  possessed,  I  believe,  almost  unrivalled  mathe- 
matical insight,  had  had  no  training  in  analysis, 
so  that  the  convenience  of  the  idea  of  action  at  a 
distance  for  purposes  of  calculation  had  no  chance 
of  mitigating  the  repugnance  he  felt  to  the  idea  of 
forces  acting  far  away  from  their  base  and  with 
no  physical  connection  with  their  origin.  He 
therefore  cast  about  for  some  way  of  picturing  to 
himself  the  actions  in  the  electric  field  which 
would  get  rid  of  the  idea  of  action  at  a  distance, 
and  replace  it  by  one  which  would  bring  into 
prominence  some  continuous  connection  between 
the  bodies  exerting  the  forces.  He  was  able  to 


g  ELECTRICITY    AND    MATTER 

do  this  by  the  conception  of  lines  of  force.  As  I 
shall  have  continually  to  make  use  of  this  method, 
and  as  I  believe  its  powers  and  possibilities  have 
never  been  adequately  realized,  I  shall  devote 
some  time  to  the  discussion  and  development  of 
this  conception  of  the  electric  field. 


FIG.  1. 

The  method  was  suggested  to  Faraday  by  the 
consideration  of  the  lines  of  force  round  a  bar 
magnet.  If  iron  filings  are  scattered  on  a  smooth 
surface  near  a  magnet  they  arrange  themselves  as 
in  Fig.  1 ;  well-marked  lines  can  be  traced  run- 


LINES    OF    FORCE  9 

ning  from  one  pole  of  the  magnet  to  the  other ; 
the  direction  of  these  lines  at  any  point  coincides 
with  the  direction  of  the  magnetic  force,  while  the 
intensity  of  the  force  is  indicated  by  the  concen- 
tration of  the  lines.  Starting  from  any  point  in 
the  field  and  travelling  always  in  the  direction  of 
the  magnetic  force,  we  shall  trace  out  a  line  which 
will  not  stop  until  we  reach  the  negative  pole  of 
the  magnet ;  if  such  lines  are  drawn  at  all  points 
in  the  field,  the  space  through  which  the  magnetic 
field  extends  wrill  be  filled  with  a  system  of  lines, 
giving  the  space  a  fibrous  structure  like  that  pos- 
sessed by  a  stack  of  hay  or  straw,  the  grain  of  the 
structure  being  along  the  lines  of  force.  I  have 
spoken  so  far  only  of  lines  of  magnetic  force ;  the 
same  considerations  will  apply  to  the  electric  field, 
and  we  may  regard  the  electric  field  as  full  of 
lines  of  electric  force,  which  start  from  positively 
and  end  on  negatively  electrified  bodies.  Up  to 
this  point  the  process  has  been  entirely  geometri- 
cal, and  could  have  been  employed  by  those  who 
looked  at  the  question  from  the  point  of  view  of 
action  at  a  distance;  to  Faraday,  however,  the 
lines  of  force  were  far  more  than  mathematical 
abstractions — they  were  physical  realities.  Fara- 
day materialized  the  lines  of  force  and  endowed 


10  ELECTRICITY   AND   MATTER 

them  with  physical  properties  so  as  to  explain  the 
phenomena  of  the  electric  field.  Thus  he  sup- 
posed that  they  were  in  a  state  of  tension,  and 
that  they  repelled  each  other.  Instead  of  an  in- 
tangible action  at  a  distance  between  two  electri- 
fied bodies,  Faraday  regarded  the  whole  space 
between  the  bodies  as  full  of  stretched  mutually 
repellent  springs.  The  charges  of  electricity  to 
which  alone  an  interpretation  had  been  given  on 
the  fluid  theories  of  electricity  were  on  this  view 
just  the  ends  of  these  springs,  and  an  electric 
charge,  instead  of  being  a  portion  of  fluid  confined 
to  the  electrified  body,  was  an  extensive  arsenal 
of  springs  spreading  out  in  all  directions  to  all 
parts  of  the  field. 

To  make  our  ideas  clear  on  this  point  let  us 
consider  some  simple  cases  from  Faraday's  point 
of  view.  Let  us  first  take  the  case  of  two  bodies 
with  equal  and  opposite  charges,  whose  lines  of 
force  are  shown  in  Fig.  2.  You  notice  that  the 
lines  of  force  are  most  dense  along  A  J3,  the  line 
joining  the  bodies,  and  that  there  are  more  lines 
of  force  on  the  side  of  A.  nearest  to  IB  than  on 
the  opposite  side.  Consider  the  effect  of  the 
lines  of  force  on  A ;  the  lines  are  in  a  state  of 
tension  and  are  pulling  away  at  A\  as  there 


LINES    OF    FORCE  H 

are  more  pulling  at  A  on  the  side  nearest  to  B 
than  on  the  opposite  side,  the  pulls  on  A  toward 
B  overpower  those  pulling  A  away  from  B,  so 
that  A  will  tend  to  move  toward  B\  it  was  in 
this  way  that  Faraday  pictured  to  himself  the 
attraction  between  oppositely  electrified  bodies. 
Let  us  now  consider  the  condition  of  one  of  the 
curved  lines  of  force,  such  as  PQ;  it  is  in  a  state 


FIG.   2. 

of  tension  and  will  therefore  tend  to  straighten 
itself,  how  is  it  prevented  from  doing  this  and 
maintained  in  equilibrium  in  a  curved  position? 
We  can  see  the  reason  for  this  if  we  remember 
that  the  lines  of  force  repel  each  other  and  that 
the  lines  are  more  concentrated  in  the  region  be- 
tween PQ  and  AB  than  on  the  other  side  of 
PQ\  thus  the  repulsion  of  the  lines  inside  PQ 
will  be  greater  than  the  repulsion  of  those  out- 
side and  the  line  PQ  will  be  bent  outwards. 


12 


ELECTRICITY    AND    MATTER 


Let  us  now  pass  from  the  case  of  two  oppositely 
electrified  bodies  to  that  of  two  similarly  elec- 
trified ones,  the  lines  of  force  for  which  are  shown 
in  Fig.  3.  Let  us  suppose  A  and  B  are  positively 
electrified;  since  the  lines  of  force  start  from 
positively  and  end  on  negatively  electrified  bodies, 
the  lines  starting  from  A  and  B  will  travel  away 
to  join  some  body  or  bodies  possessing  the 


FIG.  3. 

negative  charges  corresponding  to  the  positive 
ones  on  A  and  B;  let  us  suppose  that  these 
charges  are  a  considerable  distance  away,  so  that 
the  lines  of  force  from  A  would,  if  B  were  not 
present,  spread  out,  in  the  part  of  the  field  under 
consideration,  uniformly  in  all  directions.  Consider 
now  the  effect  of  making  the  system  of  lines  of 
force  attached  to  A  and  B  approach  each  other ; 


LINES    OF    FORCE 


13 


since  these  lines  repel  each  other  the  lines  of  force 
on  the  side  of  A  nearest  B  will  be  pushed  to  the 
opposite  side  of  A,  so  that  the  lines  of  force  will 
now  be  densest  on  the  far  side  of  A ;  thus  the 
pulls  exerted  on  A  in  the  rear  by  the  lines  of 
force  will  be  greater  than  those  in  the  front  and 
the  result  will  be  that  A  will  be  pulled  away 
from  B.  We  notice  that  the  mechanism  produc- 
ing this  repulsion  is  of  exactly  the  same  type  as 
that  which  produced  the  attraction  in  the  pre- 
vious case,  and  we  may  if  we  please  regard  the 
repulsion  between  A  and  B  as  due  to  the  attrac- 
tions on  A  and  B  of  the 
complementary  negative 
charges  which  must  exist  in 
other  parts  of  the  field. 

The  results  of  the  repul- 
sion of  the  lines  of  force 
are  clearly  shown  in  the  case 
represented  in  Fig.  4,  that 
of  two  oppositely  electrified 
plates;  you  will  notice  that 
the  lines  of  force  between 
the  plates  are  straight  except 
near  the  edges  of  the  plates ;  this  is  what  we 
should  expect  as  the  downward  pressure  exerted 


PIG.  4. 


14  ELECTRICITY    AND    MATTER 

by  the  lines  of  force  above  a  line  in  this  part  of 
the  field  will  be  equal  to  the  upward  pressure 
exerted  by  those  below  it.  For  a  line  of  force 
near  the  edge  of  the  plate,  however,  the  pressure 
of  the  lines  of  force  below  will  exceed  the  press- 
ure from  those  above,  and  the  line  of  force  will 
bulge  out  until  its  curvature  and  tension  counter- 
act the  squeeze  from  inside  ;  this  bulging  is  very 
plainly  shown  in  Fig.  4. 

So  far  our  use  of  the  lines  of  force  has  been 
descriptive  rather  than  metrical;  it  is,  however, 
easy  to  develop  the  method  so  as  to  make  it 
metrical.  We  can  do  this  by  introducing  the 
idea  of  tubes  of  force.  If  through  the  boundary 
of  any  small  closed  curve  in  the  electric  field  we 
draw  the  lines  of  force,  these  lines  will  form  a 
tubular  surface,  and  if  we  follow  the  lines  back  to 
the  positively  electrified  surface  from  which  they 
start  and  forward  on  to  the  negatively  electrified 
surface  on  which  they  end,  we  can  prove  that  the 
positive  charge  enclosed  by  the  tube  at  its  origin 
is  equal  to  the  negative  charge  enclosed  by  it  at 
its  end.  By  properly  choosing  the  area  of  the 
small  curve  through  which  we  draw  the  lines  of 
force,  we  may  arrange  that  the  charge  enclosed  by 
the  tube  is  equal  to  the  unit  charge.  Let  us  call 


LINES   OF    FORCE  15 

such  a  tube  a  Faraday  tube — then  each  unit  of 
positive  electricity  in  the  field  may  be  regarded 
as  the  origin  and  each  unit  of  negative  electricity 
as  the  termination  of  a  Faraday  tube.  We  regard 
these  Faraday  tubes  as  having  direction,  their  di- 
rection being  the  same  as  that  of  the  electric  force, 
so  that  the  positive  direction  is  from  the  positive 
to  the  negative  end  of  the  tube.  If  we  draw  any 
closed  surface  then  the  difference  between  the 
number  of  Faraday  tubes  which  pass  out  of  the 
surface  and  those  which  pass  in  will  be  equal  to  the 
algebraic  sum  of  the  charges  inside  the  surface;  this 
sum  is  what  Maxwell  called  the  electric  displace- 
ment through  the  surface.  What  Maxwell  called 
the  electric  displacement  in  any  direction  at  a 
point  is  the  number  of  Faraday  tubes  which  pass 
through  a  unit  area  through  the  point  drawn  at 
right  angles  to  that  direction,  the  number  being 
reckoned  algebraically ;  i.e.,  the  lines  which  pass 
through  in  one  direction  being  taken  as  positive, 
while  those  which  pass  through  in  the  opposite 
direction  are  taken  as  negative,  and  the  number 
passing  through  the  area  is  the  difference  between 
the  number  passing  through  positively  and  the 
number  passing  through  negatively. 

For  my  own  part,  I  have  found  the  conception 


16  ELECTRICITY    AND    MATTER 

of  Faraday  tubes  to  lend  itself  much  more  readily 
to  the  formation  of  a  mental  picture  of  the  proc- 
esses going  on  in  the  electric  field  than  that  of 
electric  displacement,  and  have  for  many  years 
abandoned  the  latter  method. 

Maxwell  took  up  the  question  of  the  ten- 
sions and  pressures  in  the  lines  of  force  in 
the  electric  field,  and  carried  the  problem  one 
step  further  than  Faraday.  By  calculating  the 
amount  of  these  tensions  he  showed  that  the 
mechanical  effects  in  the  electrostatic  field  could 
be  explained  by  supposing  that  each  Faraday 
tube  force  exerted  a  tension  equal  to  R,  R  being 
the  intensity  of  the  electric  force,  and  that,  in 
addition  to  this  tension,  there  was  in  the  medium 
through  which  the  tubes  pass  a  hydrostatic 
pressure  equal  to  %NjR,  N  being  the  density 
of  the  Faraday  tubes;  i.e.,  the  number  passing 
through  a  unit  area  drawn  at  right  angles  to 
the  electric  force.  If  we  consider  the  effect  of 
these  tensions  and  pressure  on  a  unit  volume  of 
the  medium  in  the  electric  field,  we  see  that 
they  are  equivalent  to  a  tension  ^  NH  along 
the  direction  of  the  electric  force  and  an  equal 
pressure  in  all  directions  at  right  angles  to  that 
force. 


LINES,  OF    FORCE 


17 


Moving  Faraday  Tubes 

Hitherto  we  have  supposed  the  Faraday  tubes 
to  be  at  rest,  let  us  now  proceed  to  the  study  of 
the  effects  produced  by  the  motion  of  those  tubes. 
Let  us  begin  with  the  consideration  of  a  very 
simple  case — that  of  two  parallel 
plates,  A  and  B,  charged,  one  with 
positive  the  other  with  negative 
electricity,  and  suppose  that  after 
being  charged  the  plates  are  con- 
nected by  a  conducting  wire,  E  F  G. 
This  wire  will  pass  through  some 
of  the  outlying  tubes ;  these  tubes, 
when  in  a  conductor,  contract  to 
molecular  dimensions  and  the  repul- 
sion they  previously  exerted  on 
neighboring  tubes  will  therefore 
disappear.  Consider  the  effect  of 
this  on  a  tube  PQ  between  the 
plates ;  PQ  was  originally  in  equilibrium  under 
its  own  tension,  and  the  repulsion  exerted  by  the 
neighboring  tubes.  The  repulsions  due  to  those 
cut  by  E  F  G  have  now,  however,  disappeared  so 
that  PQ  will  no  longer  be  in  equilibrium,  but  will 
be  pushed  towards  E  F  G.  Thus,  more  and  more 
tubes  will  be  pushed  into  E  FG,  and  we  shall 


}8  ELECTRICITY   AND-  MATTER 

have  a  movement  of  the  whole  set  of  tubes  be- 
tween the  plates  toward  E  F  Gr.  Thus,  while  the 
discharge  of  the  plates  is  going  on,  the  tubes  be- 
tween the  plates  are  moving  at  right  angles  to 
themselves.  What  physical  effect  accompanies 
this  movement  of  the  tubes  ?  The  result  of  con- 
necting the  plates  by  E  F  Gr  is  to  produce  a  cur- 
rent of  electricity  flowing  from  the  positively 
charged  plate  through  E  F  G  to  the  negatively 
charged  plate ;  this  is,  as  we  know,  accompanied 
by  a  magnetic  force  between  the  plates.  This 
magnetic  force  is  at  right  angles  to  the  plane  of 
the  paper  and  equal  to  4?r  times  the  intensity  of 
the  current  in  the  plate,  or,  if  <r  is  the  density  of 
the  charge  of  electricity  on  the  plates  and  v  the 
velocity  with  which  the  charge  moves,  the  mag- 
netic force  is  equal  to  4-Trcn;. 

Here  we  have  two  phenomena  which  do  not 
take  place  in  the  steady  electrostatic  field,  one  the 
movement  of  the  Faraday  tubes,  the  other 
the  existence  of  a  magnetic  force;  this  suggests 
that  there  is  a  connection  between  the  two,  and 
that  motion  of  the  Faraday  tubes  is  accompanied 
by  the  production  of  magnetic  force.  I  have  fol- 
lowed up  the  consequences  of  this  supposition  and 
have  shown  that,  if  the  connection  between  the 


LINES   OF    FORCE  19 

magnetic  force  and  the  moving  tubes  is  that  given 
below,  this  view  will  account  for  Ampere's  laws 
connecting  current  and  magnetic  force,  and  for 
Faraday's  law  of  the  induction  of  currents.  Max- 
well's great  contribution  to  electrical  theory,  that 
variation  in  the  electric  displacement  in  a  dielec- 
tric produces  magnetic  force,  follows  at  once  from 
this  view.  For,  since  the  electric  displacement  is 
measured  by  the  density  of  the  Faraday  tubes,  if 
the  electric  displacement  at  any  place  changes, 
Faraday  tubes  must  move  up  to  or  away  from  the 
place,  and  motion  of  Faraday  tubes,  by  hypoth- 
esis, implies  magnetic  force. 

The  law  connecting  magnetic  force  with  the 
motion  of  the  Faraday  tubes  is  as  follows :  A 
Faraday  tube  moving  with  velocity  v  at  a  point 
P,  produces  at  P  a  magnetic  force  whose  magni- 
tude is  4i7r  v  sin  0,  the  direction  of  the  magnetic 
force  being  at  right  angles  to  the  Faraday  tube, 
and  also  to  its  direction  of  motion  ;  0  is  the  angle 
between  the  Faraday  tube  and  the  direction  in 
which  it  is  moving.  We  see  that  it  is  only 
the  motion  of  a  tube  at  right  angles  to  itself 
which  produces  magnetic  force;  no  such  force 
is  produced  by  the  gliding  of  a  tube  along  its 
length. 


20  ELECTRICITY    AND    MATTER 

Motion  of  a  Charged  Sphere 

We  shall  apply  these  results  to  a  very  simple 
and  important  case — the  steady  motion  of  a 
charged  sphere.  If  the  velocity  of  the  sphere  is 
small  compared  with  that  of  light  then  the  Fara- 
day tubes  will,  as  when  the  sphere  is  at  rest,  be 
uniformly  distributed  and  radial  in  direction. 
They  will  be  carried  along  with  the  sphere.  If 
e  is  the  charge  on  the  sphere,  0  its  centre,  the 

X> 

density  of  the  Faraday  tubes  at  P  is  - — TT™-; 

so  that  if  v  is  the  velocity  of  the  sphere,  6  the 

,p 


FIG.   6. 

angle  between  OP  and  the  direction  of  motion  of 
the  sphere,  then,  according  to  the  above  rule,  the 

magnetic  force  at  P  will  be  €  S*n  ,  the  direc- 
tion of  the  force  will  be  at  right  angles  to  OPy 
and  at  right  angles  to  the  direction  of  motion  of 
the  sphere;  the  lines  of  magnetic  force  will  thus 


LINES   OF    FORCE  21 

be  circles,  having  their  centres  on  the  path  of  the 
centre  of  the  sphere  and  their  planes  at  right 
angles  to  this  path.  Thus,  a  moving  charge  of 
electricity  will  be  accompanied  by  a  magnetic 
field.  The  existence  of  a  magnetic  field  implies 
energy;  we  know  that  in  a  unit  volume  of  the 
field  at  a  place  where  the  magnetic  force  is  H 

there  are  ^ —  units  of  energy,  where  p,  is  the 

magnetic  permeability  of  the  medium.  In  the 
case  of  the  moving  sphere  the  energy  per  unit 

LL  r'f)      Sin     0 

volume  at  P  is  ^ — 7Tp4~-  Taking  the  sum  of 
this  energy  for  all  parts  of  the  field  outside  the 
sphere,  we  find  that  it  amounts  to  *---  ,  where  a 

is  the  radius  of  the  sphere.  If  m  is  the  mass  of 
the  sphere,  the  kinetic  energy  in  the  sphere  is 
\  <mv*',  in  addition  to  that  we  have  the  energy 
outside  the  sphere,  which  as  we  have  seen  is 

.j       0 

^ —  ;  so  that  the  whole  kinetic   energy  of  the 

(2u,  e2\ 
m  +  -^  —  }  v*,  or  the  energy  is 

the  same  as  if  the  mass  of  the  sphere  were 
m  -\ — £  --  instead  of  m.  Thus,  in  consequence  of 

u     d 


22  ELECTRICITY    AND    MATTER 

the  electric  charge,  the  mass   of  the   sphere  is 

2u  62 

measured  by  -£ — .     This  is  a  very  important  re- 

o& 

suit,  since  it  shows  that  part  of  the  mass  of  a 
charged  sphere  is  due  to  its  charge.  I  shall  later 
on  have  to  bring  before  you  considerations  which 
show  that  it  is  not  impossible  that  the  whole  mass 
of  a  body  may  arise  in  the  way. 

Before  passing  on  to  this  point,  however,  I 
should  like  to  illustrate  the  increase  which  takes 
place  in  the  mass  of  the  sphere  by  some  analogies 
drawn  from  other  branches  of  physics.  The  first  of 
these  is  the  case  of  a  sphere  moving  through  a 
frictionless  liquid.  When  the  sphere  moves  it  sets 
the  fluid  around  it  moving  with  a  velocity  propor- 
tioned to  its  own,  so  that  to  move  the  sphere  we 
we  have  not  merely  to  move  the  substance  of  the 
sphere  itself,  but  also  the  liquid  around  it ;  the 
consequence  of  this  is,  that  the  sphere  behaves  as 
if  its  mass  were  increased  by  that  of  a  certain  vol- 
ume of  the  liquid.  This  volume,  as  was  shown  by 
Green  in  1833,  is  half  the  volume  of  the  sphere. 
In  the  case  of  a  cylinder  moving  at  right  angles  to 
its  length,  its  mass  is  increased  by  the  mass  of  an 
equal  volume  of  the  liquid.  In  the  case  of  an 
elongated  body  like  a  cylinder,  the  amount  by 


LINES   OF    FORCE  23 

which  the  mass  is  increased  depends  upon  the  di- 
rection in  which  the  body  is  moving,  being  much 
smaller  when  the  body  moves  point  foremost 
than  when  moving  sideways.  The  mass  of  such 
a  body  depends  on  the  direction  in  which  it  is 
moving. 

Let  us,  however,  return  to  the  moving  electri- 
fied sphere.    We  have  seen  that  in  consequence  of 


its  charge  its  mass  is  increased  by  -—;  thus,  if  it 
is  moving  with  the  velocity  v,  the  momentum  is 
not  mv,  but  Im  +  ^  —  V^.  The  additional  mo- 

mentum -~-  v  is  not  in  the  sphere,  but  in  the  space 
od 

surrounding  the  sphere.  There  is  in  this  space 
ordinary  mechanical  momentum,  whose  resultant  is 

-|r  —  v  and  whose  direction  is  parallel  to  the  di- 

rection of  motion  of  the  sphere.  It  is  important 
to  bear  in  mind  that  this  momentum  is  not  in  any 
way  different  from  ordinary  mechanical  momen- 
tum and  can  be  given  up  to  or  taken  from  the 
momentum  of  moving  bodies.  I  want  to  bring 
the  existence  of  this  momentum  before  you  as 
vividly  and  forcibly  as  I  can,  because  the  recogni- 
tion of  it  makes  the  behavior  of  the  electric  field 


24  ELECTRICITY    AND    MATTER 

entirely  analogous  to  that  of  a  mechanical  sys- 
tem. To  take  an  example,  according 'to  Newton's 
Third  Law  of  Motion,  Action  and  Reaction  are 
equal  and  opposite,  so  that  the  momentum  in  any 
direction  of  any  self-contained  system  is  invariable. 
Now,  in  the  case  of  many  electrical  systems  there 
are  apparant  violations  of  this  principle ;  thus, 
take  the  case  of  a  charged  body  at  rest  struck  by 
an  electric  pulse,  the  charged  body  when  exposed 
to  the  electric  force  in  the  pulse  acquires  velocity 
and  momentum,  so  that  when  the  pulse  has  passed 
over  it,  its  momentum  is  not  what  it  was  origi- 
nally. Thus,  if  we  confine  our  attention  to  the 
momentum  in  the  charged  body,  i.e.,  if  we  suppose 
that  momentum  is  necessarily  confined  to  what  we 
consider  ordinary  matter,  there  has  been  a  viola- 
tion of  the  Third  Law  of  Motion,  for  the  only 
momentum  recognized  on  this  restricted  view 
has  been  changed.  The  phenomenon  is,  however, 
brought  into  accordance  with  this  law  if  we  recog- 
nize the  existence  of  the  momentum  in  the  electric 
field ;  for,  on  this  view,  before  the  pulse  reached 
the  charged  body  there  was  momentum  in  the 
pulse,  but  none  in  the  body;  after  the  pulse 
passed  over  the  body  there  was  some  momentum 
in  the  body  and  a  smaller  amount  in  the  fmlse, 


LINES   OF    FORCE  25 

the  loss  of  momentum  in  the  pulse  being  equal  to 
the  gain  of  momentum  by  the  body. 

We  now  proceed  to  consider  this  momentum 
more  in  detail.  I  have  in  my  "  Recent  Researches 
on  Electricity  and  Magnetism"  calculated  the 
amount  of  momentum  at  any  point  in  the  electric 
field,  and  have  shown  that  if  JV  is  the  number  of 
Faraday  tubes  passing  through  a  unit  area  drawn 
at  right  angles  to  their  direction,  B  the  magnetic 
induction,  9  the  angle  between  the  induction  and 
the  Faraday  tubes,  then  the  momentum  per  unit 
volume  is  equal  to  N  S  sin  0,  the  direction  of 
the  momentum  being  at  right  angles  to  the  mag- 
netic induction  and  also  to  the  Faraday  tubes. 
Many  of  you  will  notice  that  the  momentum  is 
parallel  to  what  is  known  as  Poynting's  vector — 
the  vector  whose  direction  gives  the  direction  in 
which  energy  is  flowing  through  the  field. 

Moment  of  Momentum  Due  to  cm  Electrified 
»    Point  and  a  Magnetic  Pole 

To  familiarize  ourselves  with  this  distribution 
of  momentum  let  us  consider  some  simple  cases  in 
detail.  Let  us  begin  with  the  simplest,  that  of  an 
electrified  point  and  a  magnetic  pole;  let  A,  Fig.  7, 
be  the  point,  B  the  pole.  Then,  since  the  momen- 


26  ELECTRICITY    AND   MATTER 

turn  at  any  point  P  is  at  right  angles  to  A  P,  the 
direction  of  the  Faraday  tubes  and  also  to  B  P, 
the  magnetic  induction,  we  see  that  the  momentum 
will  be  perpendicular  to  the  plane  A  B  P ;  thus, 
if  we  draw  a  series  of  lines  such  that  their  direc- 
tion at  any  point  coincides  with  the  direction  of 
the  momentum  at  that  point,  these  lines  will  form 
a  series  of  circles  whose  planes  are  perpendicular 
to  the  line  A  JB,  and  whose  centres 
lie  along  that  line.  This  distribution 
of  momentum,  as  far  as  direction 
goes,  is  that  possessed  by  a  top  spin- 
ning around  A  B.  Let  us  now  find 
what  this  distribution  of  momentum 
throughout  the  field  is  equivalent  to. 
It  is  evident  that  the  resultant 
momentum  in  any  direction  is  zero, 
but  since  the  system  is  spinning 
round  A  £,  the  direction  of  rotation  being  every- 
where the  same,  there  will  be  a  finite  moment 
of  momentum  round  A  B.  Calculating  the  value 
of  this  from  the  expression  for  the  momentum 
given  above,  we  obtain  the  very  simple  expression 
em  as  the  value  of  the  moment  of  momentum 
about  A  By  e  being  the  charge  on  the  point  and 
m  the  strength  of  the  pole.  By  means  of  this 


LINES   OF    FORCE  27 

expression  we  can  at  once  find  the  moment  of 
momentum  of  any  distribution  of  electrified  points 
and  magnetic  poles. 

To  return  to  the  system  of  the  point  and  pole, 
this  conception  of  the  momentum  of  the  system 
leads  directly  to  the  evaluation  of  the  force  acting 
on  a  moving  electric  charge  or  a  moving  magnetic 
pole.  For  suppose  that  in  the  time  8  t  the  electri- 
fied point  were  to  move  from  A  to  A! ',  the 
moment  of  momentum  is  still  em,  but 
its  axis  is  along  A'  B  instead  of  A  B. 
The  moment  of  momentum  of  the  field  \ 
has  thus  changed,  but  the  whole  moment  \ 
of  momentum  of  the  system  comprising  \ 
point,  pole,  and  field  must  be  constant,  so  \ 
that  the  change  in  the  moment  of  momen-  \ 
turn  of  the  field  must  be  accompanied  \ 
by  an  equal  and  opposite  change  in  the 
moment  of  momentum  of  the  pole  and  FlG>  8- 
point.  The  momentum  gained  by  the  point  must 
be  equal  and  opposite  to  that  gained  by  the 
pole,  since  the  whole  momentum  is  zero.  If  0  is 
the  angle  A  B  A',  the  change  in  the  moment  of 
momentum  is  em  sin  0,  with  an  axis  at  right 
angles  to  A  B  in  the  plane  of  the  paper.  Let 
8  /  be  the  change  in  the  momentum  of  A,  — 


28  ELECTRICITY   AND   MATTER 

8  I  that  of  B,  then  8  I  and  —  8  1  must  be 
equivalent  to  a  couple  whose  axis  is  at  right 
angles  to  A  B  in  the  plane  of  the  paper,  and 
whose  moment  is  e  m  sin  0.  Thus  8  I  must  be  at 
right  angles  to  the  plane  of  the  paper  and 

e  m  A  A'  sin  <t> 
87  .A±t  =  emsm0=  --  *-& 

Where   <£  is  the   angle  £  A  A.     If  v  is  the 
velocity  of  A,  A  A'=v  8  1  and  we  get 
e  m  v  sm  <  S  ^ 


AB* 

This  change  in  the  momentum  may  be  sup- 
posed due  to  the  action  of  a  force  F  perpen- 
dicular to  the  plane  of  the  paper,  F  being  the 

g     7 

rate  of  increase  of  the  momentum,  or  --r'  We  thus 


_. 
get  If  =     AB*  —  '  or         point  is  acted  on  by  a 

force  equal  to  e  multiplied  by  the  component  of 
the  magnetic  force  at  right  angles  to  the  direction 
of  motion.  The  direction  of  the  force  acting  on 
the  point  is  at  right  angles  to  its  velocity  and 
also  to  the  magnetic  force.  There  is  an  equal 
and  opposite  force  acting  on  the  magnetic  pole. 

The  value  we  have  found  for  F  is  the  ordinary 
expression  for  the  mechanical  force  acting  on  a 
moving  charged  particle  in  a  magnetic  field  ;  it 


LINES   OF    FORCE  29 

may  be  written  as  ev  H  sin  <£,  where  H's  is  the 
strength  of  the  magnetic  field.  The  force  acting 
on  unit  charge  is  therefore  v  Ifsrn  <£.  This  me- 
chanical force  may  be  thus  regarded  as  arising 
from  an  electric  force  v  H  sin  <£,  and  we  may 
express  the  result  by  saying  that  when  a  charged 
body  is  moving  in  a  magnetic  field  an  electric 
force  v  If  sin  <f>  is  produced.  This  force  is  the 
well-known  electromotive  force  of  induction  due 
to  motion  in  a  magnetic  field. 

The  forces  called  into  play  are  due  to  the 
relative  motion  of  the  pole  and  point;  if  these  are 
moving  with  the  same  velocity,  the  line  joining 
them  will  not  alter  in  direction,  the  moment  of 
momentum  of  the  system  will  remain  unchanged 
and  there  will  not  be  any  forces  acting  either  on 
the  pole  or  the  point. 

The  distribution  of  momentum  in  the  system 
of  pole  and  point  is  similar  in  some  respects  to 
that  in  a  top  spinning  about  the  line  A  B.  We 
can  illustrate  the  forces  acting  on  a  moving  elec- 
trified body  by  the  behavior  of  such  a  top.  Thus, 
let  Fig.  9  represent  a  balanced  gyroscope  spinning 
about  the  axis  A  JB,  let  the  ball  at  A  represent 
the  electrified  point,  that  at  B  the  magnetic  pole. 
Suppose  the  instrument  is  spinning  with  A  B 


30  ELECTRICITY   AND   MATTER 

horizontal,  then  if  with  a  vertical  rod  I  push 
against  A  B  horizontally,  the  point  A  will  not 
merely  move  horizontally  forward  in  the  direction 
in  which  it  is  pushed,  but  will  also  move  verti- 
cally upward  or  downward,  just  as  a  charged 


FIG.   9. 

point  would  do  if  pushed  forward  in  the  same 
way,  and  if  it  were  acted  upon  by  a  magnetic 
pole  at  JB. 

MaxweWs   Vector  Potential 

There  is  a  very  close  connection  between  the 
momentum  arising  from  an  electrified  point  and  a 


LINES   OF    FORCE  31 

magnetic  system,  and  the  Vector  Potential  of  that 
system,  a  quantity  which  plays  a  very  large  part 
in  Maxwell's  Theory  of  Electricity.  From  the  ex- 
pression we  have  given  for  the  moment  of  mo- 
mentum due  to  a  charged  point  and  a  magnetic 
pole,  we  can  at  once  find  that  due  to  a  charge  e  of 
electricity  at  a  point  P,  and  a  little  magnet  A  B  ; 
let  the  negative  pole  of  this  magnet  be  at  A,  the 
positive  at  B,  and  let  m  be  the  strength  of  either 
pole.  A  simple  calculation  shows  that  in  this 
case  the  axis  of  the  resultant  moment  of  momen- 
tum is  in  the  plane  P  A  B  at  right  angles  to  P  O, 
0  being  the  middle  point  of  A  B,  and  that  the 
magnitude  of  the  moment  of  momentum  is  equal 

to  e.m.  A  B         ^t  where  <£  is  the  angle  A  B 


makes  with  O  P.     This  moment  of  momentum  is 
equivalent  in  direction  and  magnitude  to  that  due 

to  a  momentum  e.  in.  A  B         *  at  P  directed 


at  right  angles  to  the  plane  P  A  B,  and  another 
momentum  equal  in  magnitude  and  opposite  in 

direction  at  O.     The  vector  m  A  B  at  P 


at  right  angles  to  the  plane  P  A  B  is  the  vector 
called  by  Maxwell  the  Vector  Potential  at  P  due 
to  the  Magnet. 


32  ELECTRICITY   AND   MATTER 

Calling  this  Vector  Potential  I,  we  see  that  the 
momentum  due  to  the  charge  and  the  magnet  is 
equivalent  to  a  momentum  e  /at  P  and  a  momen- 
tum —  e  ./at  the  magnet. 

We  may  evidently  extend  this  to  any  complex 
system  of  magnets,  so  that  if  /  is  the  Vector  Po- 
tential at  P  of  this  system,  the  momentum  in  the 
field  is  equivalent  to  a  momentum  e  I  at  P  to- 
gether with  momenta  at  each  of  the  magnets 
equal  to 

—  e  (Vector  Potential  at  P  due  to  that  magnet). 
If  the  magnetic  field  arises  entirely  from  electric 
currents  instead  of  from  permanent  magnets,  the 
momentum  of  a  system  consisting  of  an  electrified 
point  and  the  currents  will  differ  in  some  of  its 
features  from  the  momentum  when  the  magnetic 
field  is  due  to  permanent  magnets.  In  the  latter 
case,  as  we  have  seen,  there  is  a  moment  of  mo- 
mentum, but  no  resultant  momentum.  When, 
however,  the  magnetic  field  is  entirely  due  to 
electric  currents,  it  is  easy  to  show  that  there  is  a 
resultant  momentum,  but  that  the  moment  of  mo- 
mentum about  any  line  passing  through  the  elec- 
trified particle  vanishes.  A  simple  calculation 
shows  that  the  whole  momentum  in  the  field  is 
equivalent  to  a  momentum  e  I  at  the  electrified 


LINES   OF    FORCE  33 

point  /  being  the  Vector  Potential  at  P  due  to 
the  currents. 

Thus,  whether  the  magnetic  field  is  due  to  per- 
manent magnets  or  to  electric  currents  or  partly 
to  one  and  partly  to  the  other,  the  momentum 
when  an  electrified  point  is  placed  in  the  field  at 
P  is  equivalent  to  a  momentum  e  I  at  P  where  I 
is  .the  Vector  Potential  at  P.  If  the  magnetic 
field  is  entirely  due  to  currents  this  is  a  complete 
representation  of  the  momentum  in  the  field ;  if 
the  magnetic  field  is  partly  due  to  magnets  we 
have  in  addition  to  this  momentum  at  P  other 
momenta  at  these  magnets ;  the  magnitude  of  the 
momentum  at  any  particular  magnet  is  —  e  times 
the  Vector  Potential  at  P  due  to  that  magnet. 

The  well-known  expressions  for  the  electro- 
motive forces  due  to  Electro-magnetic  Induction 
follow  at  once  from  this  result.  For,  from  the 
Third  Law  of  Motion,  the  momentum  of  any  self- 
contained  system  must  be  constant.  Now  the 
momentum  consists  of  (1)  the  momentum  in  the 
field ;  (2)  the  momentum  of  the  electrified  point, 
and  (3)  the  momenta  of  the  magnets  or  circuits 
carrying  the  currents.  Since  (1)  is  equivalent  to 
a  momentum  e  1  at  the  electrified  particle,  we  see 
that  changes  in  the  momentum  of  the  field  must 


34  ELECTRICITY   AND   MATTER 

be  accompanied  by  changes  in  the  momentum  of 
the  particle.  Let  M  be  the  mass  of  the  electrified 
particle,  u,  v,  w  the  components  parallel  to  the 
axes  of  a?,  y,  z  of  its  velocity,  F,  G,  U,  the  com- 
ponents parallel  to  these  axes  of  the  Vector  Po- 
tential at  Pj  then  the  momentum  of  the  field  is 
equivalent  to  momenta  e  F,  e  6r,  e  H  at  P  parallel 
to  the  axes  of  #?,  y,  2 ;  and  the  momentum  of  the 
charged  point  at  P  has  for  components  Mu,  Mo, 
Mw.  As  the  momentum  remains  constant,  M u  + 
e  F  is  constant,  hence  if  8  u  and  S  F  are  simulta- 
neous changes  in  u  and  F, 

MSu  +  eSF=  0; 

du  dF 

or  m-=-=  —  e  -j-;  . 
at  dt 

From  this  equation  we  see  that  the  point  with  the 
charge  behaves  as  if  it  were  acted  upon  by  a  me. 
chanical  force  parallel  to  the  axis  of  x  and  equal  to 

/7  T/7  rJ  W 

—  e  -=— ,  i.e..  by  an  electric  force  equal  to  —  ~^— 
dt'  dt- 

In  a  similar  way  we  see  that  there  are  electric 
forces  -  -j — ?  _  -j— ,  parallel  to  y  and  z  respec- 

Cu  t  Cu  t 

tively.  These  are  the  well-known  expressions  of 
the  forces  due  to  electro-magnetic  induction,  and 
we  see  that  they  are  a  direct  consequence  of  the 


LINES    OF    FORCE  35 

principle  that  action  and  reaction  are  equal  and 
opposite. 

Eeaders  of  Faraday's  Experimental  Researches 
will  remember  that  he  is  constantly  referring  to 
what  he  called  the  "  Electrotonic  State  "  ;  thus  he 
regarded  a  wire  traversed  by  an  electric  current 
as  being  in  the  Electrotonic  State  when  in  a 
magnetic  field.  No  effects  due  to  this  state  can  be 
detected  as  long  as  the  field  remains  constant ;  it 
is  when  it  is  changing  that  it  is  operative.  This 
Electrotonic  State  of  Faraday  is  just  the  momen- 
tum existing  in  the  field. 


CHAPTEK  II 

ELECTRICAL  AND   BOUND   MASS. 

I  WISH  in  this  chapter  to  consider  the  connec- 
tion between  the  momentum  in  the  electric  field 
and  the  Faraday  tubes,  by  which,  as  I  showed  in 
the  last  lecture,  we  can  picture  to  ourselves  the 
state  of  such  a  field.  Let  us  begin  by  considering 
the  case  of  the  moving  charged  sphere.  The  lines 
of  electric  force  are  radial ;  those  of  magnetic  force 
are  circles  having  for  a  common  axis  the  line  of  mo- 
tion of  the  centre  of  the  sphere ;  the  momentum 

at  a  point  P  is  at  right 
angles  to  each  of  these 
directions  and  so  is  at 
right  angles  to  O  P  in 
the  plane  containing  P 
and  the  line  of  motion 
FlG-  1(X  of  the  centre  of  the 

sphere.  If  the  number  of  Faraday  tubes  passing 
through  a  unit  area  at  P  placed  at  right  angles 
to  0  P  is  JVJ  the  magnetic  induction  at  P  is, 
if  fji  is  the  magnetic  permeability  of  the  medium 


ELECTRICAL   MASS  37 

surrounding  the  sphere,  ^tr^Nv  sin  0,  v  being 
the  velocity  of  the  sphere  and  9  the  angle 
O  P  makes  with  the  direction  of  motion  of 
the  sphere.  By  the  rule  given  on  page  25  the 
momentum  in  unit  volume  of  the  medium  at  P  is 
N  y.  ^TrpNv  sin  0,  or  ^irpN^v  sin  0,  and  is 
in  the  direction  of  the  component  of  the  veloc- 
ity of  the  Faraday  tubes  at  right  angles  to  their 
length.  Now  this  is  exactly  the  momentum  which 
would  be  produced  if  the  tubes  were  to  carry 
with  them,  when  they  move  at  right  angles  to 
their  length,  a  mass  of  the  surrounding  medium 
equal  to  47T  p  N*  per  unit  volume,  the  tubes  pos- 
sessing no  mass  themselves  and  not  carrying  any 
of  the  medium  with  them  when  they  glide 
through  it  parallel  to  their  own  length.  We 
suppose  in  fact  the  tubes  to  behave  very  much  as 
long  and  narrow  cylinders  behave  when  moving 
through  water  ;  these  if  moving  endwise,  i.e.,  par- 
allel to  their  length,  carry  very  little  water  along 
with  them,  while  when  they  move  sideways,  i.e.,  at 
right  angles  to  their  axis,  each  unit  length  of  the 
tube  carries  with  it  a  finite  mass  of  water.  When 
the  length  of  the  cylinder  is  very  great  compared 
with  its  breadth,  the  mass  of  water  carried  by  it 
when  moving  endwise  may  be  neglected  in  com- 


38  ELECTRICITY   AND    MATTER 

parison  with  that  carried  by  it  when  moving  side- 
ways ;  if  the  tube  had  no  mass  beyond  that  which 
it  possesses  in  virtue  of  the  water  it  displaces,  it 
would  have  mass  for  sideways  but  none  for  end- 
wise motion. 

We  shall  call  the  mass  4?r  p,  Nz  carried  by  the 
tubes  in  unit  volume  the  mass  of  the  bound  ether. 
It  is  a  very  suggestive  fact  that  the  electrostatic 
energy  E  in  unit  volume  is  proportional  to  M  the 
mass  of  the  bound  ether  in  that  volume.  This  can 

easily  be  proved  as  follows  :   E  =    ff      ,  where 

_/L 

K  is  the  specific  inductive  capacity  of  the 
medium  ;  while  M  —  4?r  p,  N*,  thus, 

W       1    M  • 

&  =  i  —  jrr; 

i  / 

but  —jr  =  V*  where  V  is  the  velocity  with  which 
light  travels  through  the  medium,  hence 


thus  E  is  equal  to  the  kinetic  energy  possessed 
by  the  bound  mass  when  moving  with  the  veloc- 
ity of  light. 

The  mass  of  the  bound  ether  in  unit  volume  is 
4?r  ft  -ZV^2  where  N\&  the  number  of  Faraday  tubes  ; 
thus,  the  amount  of  bound  mass  per  unit  length  of 


ELECTRICAL   MASS  39 

each  Faraday  tube  is  ±TT  pN.  We  have  seen  that 
this  is  proportional  to  the  tension  in  each  tube,  so 
that  we  may  regard  the  Faraday  tubes  as  tightly 
stretched  strings  of  variable  mass  and  tension ;  the 
tension  being,  however,  always  proportional  to  the 
mass  per  unit  length  of  the  string. 

Since  the  mass  of  ether  imprisoned  by  a  Faraday 
tube  is  proportional  to  JVthe  number  of  Faraday 
tubes  in  unit  volume,  we  see  that  the  mass  and 
momentum  of  a  Faraday  tube  depend  not  merely 
upon  the  configuration  and  velocity  of  the  tube 
under  consideration,  but  also  upon  the  number 
and  velocity  of  the  Faraday  tubes  in  its  neigh- 
borhood. We  have  many  analogies  to  this  in  the 
case  of  dynamical  systems  ;  thus,  in  the  case  of  a 
number  of  cylinders  with  their  axes  parallel,  mov- 
ing about  in  an  incompressible  liquid,  the  momen- 
tum of  any  cylinder  depends  upon  the  positions 
and  velocities  of  the  cylinders  in  its  neighborhood. 
The  following  hydro-dynamical  system  is  one  by 
which  we  may  illustrate  the  fact  that  the  bound 
mass  is  proportional  to  the  square  of  the  number 
of  Faraday  tubes  per  unit  volume. 

Suppose  we  have  a  cylindrical  vortex  column  of 
strength  m  placed  in  a  mass  of  liquid  whose  ve- 
locity, if  not  disturbed  by  the  vortex  column,  would 


40 


ELECTRICITY    AND    MATTER 


be  constant  both  in  magnitude  and  direction,  and 
at  right  angles  to  the  axis  of  the  vortex  column. 
The  lines  of  flow  in  such  a  case  are  represented 
in  Fig.  11,  where  A  is  the  section  of  the  vortex 


FIG.  11. 

column  whose  axis  is  supposed  to  be  at  right  an- 
gles to  the  plane  of  the  paper.  We  see  that  some 
of  these  lines  in  the  neighborhood  of  the  column 
are  closed  curves.  Since  the  liquid  does  not  cross 
the  lines  of  flow,  the  liquid  inside  a  closed  curve 
will  always  remain  in  the  neighborhood  of  the  col- 
umn and  will  move  with  it.  Thus,  the  column 
will  imprison  a  mass  of  liquid  equal  to  that  en- 
closed by  the  largest  of  the  closed  lines  of  flow. 
If  m  is  the  strength  of  the  vortex  column  and  a  the 
velocity  of  the  undisturbed  flow  of  the  liquid,  we 
can  easily  show  that  the  mass  of  liquid  imprisoned 


ELECTRICAL   MASS  4j 

by  the  column   is  proportional  to  ^.      Thus,  if 

we  take  m  as  proportional  to  the  number  of 
Faraday  tubes  in  unit  area,  the  system  illustrates 
the  connection  between  the  bound  mass  and  the 
strength  of  the  electric  field. 

Effective  of  Velocity  on  the  Sound  Mass 

I  will  now  consider  another  consequence  of  the 
idea  that  the  mass  of  a  charged  particle  arises  from 
the  mass  of  ether  bound  by  the  Faraday  tube  as- 
sociated with  the  charge.  These  tubes,  when  they 
move  at  right  angles  to  their  length,  carry  with 
them  an  appreciable  portion  of  the  ether  through 
which  they  move,  while  when  they  move  parallel 
to  their  length,  they  glide  through  the  fluid  with- 
out setting  it  in  motion.  Let  us  consider  how  a 
long,  narrow  cylinder,  shaped  like  a  Faraday  tube, 
would  behave  when  moving  through  a  liquid. 

Such  a  body,  if  free  to  twist  in  any  direction, 
will  not,  as  you  might  expect  at  first  sight,  move 
point  foremost,  but  will,  on  the  contrary,  set  itself 
broadside  to  the  direction  of  motion,  setting  itself 
so  as  to  carry  with  it  as  much  of  the  fluid  through 
which  it  is  moving  as  possible.  Many  illustra- 
tions of  this  principle  could  be  given,  one  very 


42  ELECTRICITY   AND   MATTER 

familiar  one  is  that  falling  leaves  do  not  fall  edge 
first,  but  flutter  down  with  their  planes  more  or 
less  horizontal. 

If  we  apply  this  principle  to  the  charged  sphere, 
we  see  that  the  Faraday  tubes  attached  to  the 
sphere  will  tend  to  set  themselves  at  right  angles 
to  the  direction  of  motion  of  the  sphere,  so  that  if 
this  principle  were  the  only  thing  to  be  considered 
all  the  Faraday  tubes  would  be  forced  up  into  the 
equatorial  plane,  i.e.,  the  plane  at  right  angles  to 
the  direction  of  motion  of  the  sphere,  for  in  this 
position  they  would  all  be  moving  at  right  angles 
to  their  lengths.  We  must  remember,  however, 
that  the  Faraday  tubes  repel  each  other,  so  that 
if  they  were  crowded  into  the  equatorial  region 
the  pressure  there  would  be  greater  than  that 
near  the  pole.  This  would  tend  to  thrust  the 
Faraday  tubes  back  into  the  position  in  which  they 
are  equally  distributed  all  over  the  sphere.  The 
actual  distribution  of  the  Faraday  tubes  is  a  com- 
promise between  these  extremes.  They  are  not 
all  crowded  into  the  equatorial  plane,  neither  are 
they  equally  distributed,  for  they  are  more  in  the 
equatorial  regions  than  in  the  others  ;  the  excess  of 
the  density  of  the  tubes  in  these  regions  increasing 
with  the  speed  with  which  the  charge  is  moving. 


ELECTRICAL    MASS  43 

When  a  Faraday  tube  is  in  the  equatorial  region 
it  imprisons  more  of  the  ether  than  when  it  is 
near  the  poles,  so  that  the  displacement  of  the 
Faraday  tubes  from  the  pole  to  the  equator  will 
increase  the  amount  of  ether  imprisoned  by  the 
tubes,  and  therefore  the  mass  of  the  body. 

It  has  been  shown  (see  Heaviside,  Phil.  Mag., 
April,  1889,  "Recent  Researches,"  p.  19)  that  the 
effect  of  the  motion  of  the  sphere  is  to  displace 
each  Faraday  tube  toward  the  equatorial  plane, 
i.e.,  the  plane  through  the  centre  of  the  sphere  at 
right  angles  to  its  direction  of  motion,  in  such  a 
way  that  the  projection  of  the  tube  on  this  plane 
remains  the  same  as  for  the  uniform  distribution  of 
tubes,  but  that  the  distance  of  every  point  in  the 
tube  from  the  equatorial  plane  is  reduced  in  the 
proportion  of  V  V*-  v*  to  V,  where  V  is  the  veloc- 
ity of  light  through  the  medium  and  v  the  velocity 
of  the  charged  body. 

From  this  result  we  see  that  it  is  only  when  the 
velocity  of  the  charged  body  is  comparable  with 
the  velocity  of  light  that  the  change  in  distribu- 
tion of  the  Faraday  tubes  due  to  the  motion  of 
the  body  becomes  appreciable. 

In  "  Recent  Researches  on  Electricity  and  Mag- 
netism," p.  21, 1  calculated  the  momentum  I,  in  the 


44  ELECTRICITY    AND    MATTER 

space  surrounding  a  sphere  of  radius  a,  having  its 
centre  at  the  moving  charged  body,  and  showed  that 
the  value  of  /is  given  by  the  following  expression  : 


where  as  before  v  and  V  are  respectively  the  ve- 
locities of  the  particle  and  the  velocity  of  light, 
and  0  is  given  by  the  equation 

sin  6  =  T^. 

The  mass  of  the  sphere  is  increased  in  conse- 
quence of  the  charge  by  -,and  thus  we  see  from 

equation  (1)  that  for  velocities  of  the  charged 
body  comparable  with  that  of  light  the  mass  of 
the  body  will  increase  with  the  velocity.  It  is 
evident  from  equation  (1)  that  to  detect  the  influ- 
ence of  velocity  on  mass  we  must  use  exceed- 
ingly small  particles  moving  with  very  high  ve- 
locities. Now,  particles  having  masses  far  smaller 
than  the  mass  of  any  known  atom  or  molecule 
are  shot  out  from  radium  with  velocities  ap- 
proaching in  some  cases  to  that  of  light,  and  the 
ratio  of  the  electric  charge  to  the  mass  for  parti- 


ELECTRICAL   MASS  45 

cles  of  this  kind  has  lately  been  made  the  subject 
of  a  very  interesting  investigation  by  Kaufmann, 
with  the  results  shown  in  the  following  table ;  the 
first  column  contains  the  values  of  the  velocities 
of  the  particle  expressed  in  centimetres  per  sec- 
ond, the  second  column  the  value  of  the  fraction 

a 

—  where  e  is  the  charge  and  m  the  mass  of  the 
particle : 

v  X  10-10  ^  X  10-7 

2.83  .62 

2.72  .77 

2.59  .975 

2.48  1.17 

2.36  1.31 

a 

We  see  from  these  values  that  the  value  of  —  di- 

m 

minishes  as  the  velocity  increases,  indicating,  if 
we  suppose  the  charge  to  remain  constant,  that 
the  mass  increases  with  the  velocity.  Kaufmann's 
results  give  us  the  means  of  comparing  the  part  of 
the  mass  due  to  the  electric  charge  with  the  part 
independent  of  the  electrification ;  the  second 
part  of  the  mass  is  independent  of  the  velocity. 
If  then  we  find  that  the  mass  varies  appreciably 
with  the  velocity,  we  infer  that  the  part  of  the 


46  ELECTRICITY    AND    MATTER 

mass  due  to  the  charge  must  be  appreciable  in 
comparison  with  that  independent  of  it.  To  cal- 
culate the  effect  of  velocity  on  the  mass  of  an 
electrified  system  we  must  make  some  assump- 
tion as  to  the  nature  of  the  system,  for  the  effect 
on  a  charged  sphere  for  example  is  not  quite  the 
same  as  that  on  a  charged  ellipsoid  ;  but  having 
made  the  assumption  and  calculated  the  theoretical 
effect  of  the  velocity  on  the  mass,  it  is  easy  to  de- 
duce the  ratio  of  the  part  of  the  mass  independent 
of  the  charge  to  that  part  which  at  any  velocity  de- 
pends upon  the  charge.  Suppose  that  the  part 
of  the  mass  due  to  electrification  is  at  a  velocity 
v  equal  to  m0f(v)  where  f(v)  is  a  known  function 
of  v,  then  if  MV1  Mvi  are  the  observed  masses  at 
the  velocities  v  and  vl  respectively  and  M  the  part 
of  the  mass  independent  of  charge,  then 


two  equations  from  which  M  and  m0  can  be  de- 
termined. Kaufmann,  on  the  assumption  that 
the  charged  body  behaved  like  a  metal  sphere, 
the  distribution  of  the  lines  of  force  of  which 
when  moving  has  been  determined  by  G.  F.  C. 
Searle,  came  to  the  conclusion  that  when  the  parti- 
cle was  moving  slowly  the  "  electrical  mass  "  was 


ELECTRICAL   MASS  47 

about  one-fourth  of  the  whole  mass.  He  was  care- 
ful to  point  out  that  this  fraction  depends  upon 
the  assumption  we  make  as  to  the  nature  of  the 
moving  body,  as,  for  example,  whether  it  is  spheri- 
cal or  ellipsoidal,  insulating  or  conducting;  and 
that  with  other  assumptions  his  experiments  might 
show  that  the  whole  mass  was  electrical,  which  he 
evidently  regarded  as  the  most  probable  result. 

In  the  present  state  of  our  knowledge  of  the 
constitution  of  matter,  I  do  not  think  anything  is 
gained  by  attributing  to  the  small  negatively 
charged  bodies  shot  out  by  radium  and  other 
bodies  the  property  of  metallic  conductivity,  and 
I  prefer  the  simpler  assumption  that  the  distribu- 
tion of  the  lines  of  force  round  these  particles  is 
the  same  as  that  of  the  lines  due  to  a  charged 
point,  provided  we  confine  our  attention  to  the 
field  outside  a  small  sphere  of  radius  a  having  its 
centre  at  the  charged  point ;  on  this  supposition 
the  part  of  the  mass  due  to  the  charge  is  the  value 

of  --  in  equation  (1)  on  page  44.  I  have  calcu- 
lated from  this  expression  the  ratio  of  the  masses 
of  the  rapidly  moving  particles  given  out  by  ra- 
dium to  the  mass  of  the  same  particles  when  at 
rest,  or  moving  slowly,  on  the  assumption  that  the 


48  ELECTRICITY    AND    MATTER 

whole  of  the  mass  is  due  to  the  charge  and  have  com- 
pared these  results  with  the  values  of  the  same 
ratio  as  determined  by  Kaufmann's  experiments. 
These  results  are  given  in  Table  (II),  the  first  col- 
umn of  which  contains  the  values  of  v9  the  veloci- 
ties of  the  particles ;  the  second  p,  the  number  of 
times  the  mass  of  a  particle  moving  with  this  ve- 
locity exceeds  the  mass  of  the  same  particle  when 
at  rest,  determined  by  equation  (1) ;  the  third 
column  p1,  the  value  of  this  quantity  found  by 
Kaufmann  in  his  experiments. 

TABLE  II. 

v  X  10-10  — 
sec 

2.85 
2.72 
2.59 
2.48 
2.36 

These  results  support  the  view  that  the  whole 
mass  of  these  electrified  particles  arises  from  their 
charge. 

We  have  seen  that  if  we  regard  the  Faraday 
tubes  associated  with  these  moving  particles  as 
being  those  due  to  a  moving  point  charge,  and 


P 

P1 

3.1 

3.09 

2.42 

2.43 

2.0 

2.04 

1.66 

1.83 

1.5 

1.65 

ELECTRICAL   MASS  49 

confine  our  attention  to  the  part  of  the  field  which 
is  outside  a  sphere  of  radius  a  concentric  with  the 
charge,  the  mass  m  due  to  the  charge  e  on  the 
particle  is,  when  the  particle  is  moving  slowly, 

given  by  the  equation  m  =  -~  —  • 

In  a  subsequent  lecture  I  will  explain 
how  the  values  of  me  and  e  have  been  deter- 
mined ;  the  result  of  these  determinations  is  that 

-  =  10-T  and  e  =  1.2  X  10'20  in  C.  G.  S.  elec- 
e 

trostatic  units.  Substituting  these  values  in  the 
expression  for  m  we  find  that  a  is  about  5  X 
10~14  cm,  a  length  very  small  in  comparison  with 
the  value  10~8  c  m,  which  is  usually  taken  as  a  good 
approximation  to  the  dimensions  of  a  molecule. 

We  have  regarded  the  mass  in  this  case  as  due 
to  the  mass  of  ether  carried  along  by  the  Faraday 
tubes  associated  with  the  charge.  As  these  tubes 
stretch  out  to  an  infinite  distance,  the  mass  of  the 
particle  is  as  it  were  diffused  through  space,  and 
has  no  definite  limit.  In  consequence,  however,  of 
the  very  small  size  of  the  particle  and  the  fact 
that  the  mass  of  ether  carried  by  the  tubes  (being 
proportional  to  the  square  of  the  density  of  the 
Faraday  tubes)  varies  inversely  as  the  fourth 


50  ELECTRICITY   AND   MATTER 

power  of  the  distance  from  the  particle,  we  find 
by  a  simple  calculation  that  all  but  the  most  insig- 
nificant fraction  of  mass  is  confined  to  a  distance 
from  the  particle  which  is  very  small  indeed  com- 
pared with  the  dimensions  ordinarily  ascribed  to 
atoms. 

In  any  system  containing  electrified  bodies  a 
part  of  the  mass  of  the  system  will  consist  of  the 
mass  of  the  ether  carried  along  by  the  Faraday 
tubes  associated  with  the  electrification.  Now 
one  view  of  the  constitution  of  matter — a  view,  I 
hope  to  discuss  in  a  later  lecture — is  that  the 
atoms  of  the  various  elements  are  collections  of 
positive  and  negative  charges  held  together  mainly 
by  their  electric  attractions,  and,  moreover,  that 
the  negatively  electrified  particles  in  the  atom 
(corpuscles  I  have  termed  them)  are  identical 
with  those  small  negatively  electrified  particles 
whose  properties  we  have  been  discussing.  On 
this  view  of  the  constitution  of  matter,  part 
of  the  mass  of  any  body  would  be  the  mass  of 
the  ether  dragged  along  by  the  Faraday  tubes 
stretching  across  the  atom  between  the  positively 
and  negatively  electrified  constituents.  The  view 
I  wish  to  put  before  you  is  that  it  is  not  merely  a 
part  of  the  mass  of  a  body  which  arises  in  this 


ELECTRICAL   MASS  51 

way,  but  that  the  whole  mass  of  any  body  is  just 
the  mass  of  ether  surrounding  the  body  which  is 
carried  along  by  the  Faraday  tubes  associated 
with  the  atoms  of  the  body.  In  fact,  that  all  mass 
is  mass  of  the  ether,  all  momentum,  momentum  of 
the  ether,  and  all  kinetic  energy,  kinetic  energy 
of  the  ether.  This  view,  it  should  be  said,  requires 
the  density  of  the  ether  to  be  immensely  greater 
than  that  of  any  known  substance. 

It  might  be  objected  that  since  the  mass  has  to 
be  carried  along  by  the  Faraday  tubes  and  since 
the  disposition  of  these  depends  upon  the  relative 
position  of  the  electrified  bodies,  the  mass  of  a 
collection  of  a  number  of  positively  and  negatively 
electrified  bodies  would  be  constantly  changing 
with  the  positions  of  these  bodies,  and  thus  that 
mass  instead  of  being,  as  observation  and  experi- 
ment have  shown,  constant  to  a  very  high  degree 
of  approximation,  should  vary  with  changes  in 
the  physical  or  chemical  state  of  the  body. 

These  objections  do  not,  however,  apply  to  such 
a  case  as  that  contemplated  in  the  preceding  theory, 
where  the  dimensions  of  one  set  of  the  electrified 
bodies — the  negative  ones — are  excessively  small 
in  comparison  with  the  distances  separating  the 
various  members  of  the  system  of  electrified  bodies. 


52  ELECTRICITY   AND   MATTER 

When  this  is  the  case  the  concentration  of  the 
lines  of  force  on  the  small  negative  bodies — the 
corpuscles — is  so  great  that  practically  the  whole 
of  the  bound  ether  is  localized  around  these 
bodies,  the  amount  depending  only  on  their  size 
and  charge.  Thus,  unless  we  alter  the  number  or 
character  of  the  corpuscles,  the  changes  occurring 
in  the  mass  through  any  alteration  in  their  rela- 
tive positions  will  be  quite  insignificant  in  com- 
parison with  the  mass  of  the  body. 


CHAPTER  III 

EFFECTS   DUE  TO   ACCELERATION    OF  THE 
FARADAY  TUBES 

Rantgen  Hays  and  Liglit 

WE  have  considered  the  behavior  of  the  lines 
of  force  when  at  rest  and  when  moving  uniformly, 
we  shall  in  this  chapter  consider  the  phenomena 
which  result  when  the  state  of  motion  of  the  lines 
is  changing. 

Let  us  begin  with  the  case  of  a  moving  charged 
point,  moving  so  slowly  that  the  lines  of  force  are 
uniformly  distributed  around  it,  and  consider  what 
must  happen  if  we  suddenly  stop  the  point.  The 
Faraday  tubes  associated  with  the  sphere  have 
inertia;  they  are  also  in  a  state  of  tension,  the 
tension  at  any  point  being  proportional  to  the  mass 
per  unit  length.  Any  disturbance  communicated 
to  one  end  of  the  tube  will  therefore  travel  along 
it  with  a  constant  and  finite  velocity  ;  the  tube  in 
fact  having  very  considerable  analogy  with  a 
stretched  string.  Suppose  we  have  a  tightly 
stretched  vertical  string  moving  uniformly,  from 


54 


ELECTRICITY    AND    MATTER 


right  to  left,  and  that  we  suddenly  stop  one  end, 
A,  what  will  happen  to  the  string  ?  The  end  A 
will  come  to  rest  at  once,  but  the  forces  called 
into  play  travel  at  a  finite  rate,  and  each  part  of 
the  string  will  in  virtue  of  its  inertia  continue  to 
move  as  if  nothing  had  happened  to  the  end  A 
until  the  disturbance  starting  from  A  reaches  it. 
Thus,  if  V  is  the  velocity  with  which  a  disturb- 
ance travels  along  the  string,  then  when  a  time,  t, 
has  elapsed  after  the  stoppage  of  A,  the  parts  of 
the  string  at  a  greater  distance  than  Vt  from  A 
will  be  unaffected  by  the  stoppage,  and  will  have 
the  position  and  velocity  they  would  have  had 
if  the  string  had  continued  to  move  uniformly 
forward.  The  shape  of  the  string  at  successive 
intervals  will  be  as  shown  in  Fig.  12,  the  length  of 


j 


A 
FIG.  12. 


the  horizontal  portion  increasing  as   its  distance 
from  the  fixed  end  increases. 


RONTGEN    RAYS   AND   LIGHT  55 

Let  us  now  return  to  the  case  of  the  moving 
charged  particle  which  we  shall  suppose  suddenly 
brought  to  rest,  the  time  occupied  by  the  stoppage 
being  T.  To  find  the  configuration  of  the  Faraday 
tubes  after  a  time  t  has  elapsed  since  the  beginning 
of  the  process  of  bringing  the  charged  particle  to 
rest,  describe  with  the  charged  particle  as  centre 
two  spheres,  one  having  the  radius  Vt,  the  other 
the  radius  V(t  —  T),  then,  since  no  disturbance  can 
have  reached  the  Faraday  tubes  situated  outside 
the  outer  sphere,  these  tubes  will  be  in  the  posi- 
tion they  would  have  occupied  if  they  had  moved 
forward  with  the  velocity  they  possessed  at  the 
moment  the  particle  was  stopped,  while  inside  the 
inner  sphere,  since  the  disturbance  has  passed 
over  the  tubes,  they  will  be  in  their  final  positions. 
Thus,  consider  a  tube  which,  when  the  particle 
was  stopped  was  along  the  line  OPQ  (Fig.  13) ; 
this  will  be  the  final  position  of  the  tube ;  hence  at 
the  time  t  the  portion  of  this  tube  inside  the  inner 
sphere  will  occupy  the  position  OP,  while  the 
portion  P'  Q'  outside  the  outer  sphere  will  be  in  the 
position  it  would  have  occupied  if  the  particle  had 
not  been  reduced  to  rest,  i.e.,  if  O '  is  the  position 
the  particle  would  have  occupied  if  it  had  not 
been  stopped,  P ' Q,'  will  be  a  straight  line  pass- 


56  ELECTRICITY    AND    MATTER 

ing  through  Of.  Thus,  to  preserve  its  continuity 
the  tube  must  bend  round  in  the  shell  between  the 
two  spheres,  and  thus  be  distorted  into  the  shape 
OPP'Q'.  Thus,  the  tube  which  before  the  stop- 


FIG.  13. 

page  of  the  particle  was  radial,  has  now  in  the 
shell  a  tangential  component,  and  this  tangential 
component  implies  a  tangential  electric  force. 
The  stoppage  of  the  particle  thus  produces  a 
radical  change  in  the  electric  field  due  to  the  par- 
ticle, and  gives  rise,  as  the  following  calculation 
will  show,  to  electric  and  magnetic  forces  much 
greater  than  those  existing  in  the  field  when  the 
particle  was  moving  steadily. 

If  we  suppose  that  the  thickness  8  of  the  shell 
is  so  small  that  the  portion  of  the  Faraday  tube 
inside  it  may  be  regarded  as  straight,  then  if  T  is 


RONTGEN   RAYS    AND   LIGHT  57 

the  tangential  electric  force  inside  the  pulse,  R 
the  radial  force,  we  have 

T_   P'Jg  __  00' sin  0  _  ^  sin  0 
It ~  PR  ~~          8  8      ' 

Where  v  is  the  velocity  with  which  the  particle 
was  moving  before  it  was  stopped,  0  the  angle 
OP  makes  with  the  direction  of  motion  of  the 
particle,  t  the  time  which  has  elapsed  since  the  par- 

S) 

tide  was  stopped ;  since  R  =  -Typ*  and  (9  P  =  Vt 
where  "Pis  the  velocity  of  light,  we  have,  if  r  =  OP, 

T_  ev  sin  0  ,  , 

V  TT- 

The  tangential  Faraday  tubes  moving  forward 
with  the  velocity  "Fwill  produce  at  P  a  magnetic 
force  H  equal  to  V  T,  this  force  will  be  at  right 
angles  to  the  plane  of  the  paper  and  in  the 
opposite  direction  to  the  magnetic  force  existing 
at  P  before  the  stoppage  of  the  particle ;  since  its 
magnitude  is  given  by  the  equation, 

-u      e  v  sin  9 

±1  = s — , 

ro 

e  v  sin  9         .      -, 
it  exceeds  the  magnetic  torce g —  previously 

existing  in  the  proportion  of  r  to  8.     Thus,  the 


58  ELECTRICITY    AND    MATTER 

pulse  produced  by  the  stoppage  of  the  particle  is 
the  seat  of  intense  electric  and  magnetic  forces 
which  diminish  inversely  as  the  distance  from  the 
charged  particle,  whereas  the  forces  before  the 
particle  was  stopped  diminished  inversely  as  the 
square  of  the  distance ;  this  pulse  travelling  out- 
ward with  the  velocity  of  light  constitutes  in  my 
opinion  the  Rontgen  rays  which  are  produced 
when  the  negatively  electrified  particles  which 
form  the  cathode  rays  are  suddenly  stopped  by 
striking  against  a  solid  obstacle. 

The  energy  in  the  pulse  can  easily  be  shown 

to  be  equal  to 

2  6V 

3CN      J 
0 

this  energy  is  radiated  outward  into  space. 
The  amount  of  energy  thus  radiated  depends 
upon  S,  the  thickness  of  the  pulse,  i.  e.,  upon 
the  abruptness  with  which  the  particle  is 
stopped;  if  the  particle  is  stopped  instantaneously 
the  whole  energy  in  the  field  will  be  absorbed  in 
the  pulse  and  radiated  away,  if  it  is  stopped  grad- 
ually only  a  fraction  of  the  energy  will  be  radiated 
into  space,  the  remainder  will  appear  as  heat  at 
the  place  where  the  cathode  rays  were  stopped. 
It  is  easy  to  show  that  the  momentum  in  the 


RONTGEN   RAYS    AND   LIGHT  59 

pulse  at  any  instant  is  equal  and  opposite  to  the 
momentum  in  the  field  outside  the  pulse ;  as  there 
is  no  momentum  in  the  space  through  which  the 
pulse  has  passed,  the  whole  momentum  in  the  field 
after  the  particle  is  stopped  is  zero. 

The  preceding  investigation  only  applies  to  the 
case  when  the  particle  was  moving  so  slowly  that 
the  Faraday  tubes  before  the  stoppage  of  the 
pulse  were  uniformly  distributed;  the  same 
principles,  however,  will  give  us  the  effect  of 
stopping  a  charged  particle  whenever  the  dis- 
tribution of  the  Faraday  tubes  in  the  state  of 
steady  motion  has  been  determined. 

Let  us  take,  for  example,  the  case  when  the 
particle  was  initially  moving  with  the  velocity  of 
light;  the  rule  stated  on  page  43  shows  that 
before  the  stoppage  the  Faraday  tubes  were 
all  congregated  in  the  equatorial  plane  of  the 
moving  particle.  To  find  the  configuration  of 
the  Faraday  tubes  after  a  time  t  we  proceed  as 
before  by  finding  the  configuration  at  that  time 
of  the  tubes,  if  the  particle  had  not  been  stopped. 
The  tubes  would  in  that  case  have  been  in  a  plane 
at  a  distance  Vt  in  front  of  the  particle.  Draw 
two  spheres  having  their  centres  at  the  particle  and 
having  radii  respectively  equal  to  Vt  and  V  (t  —  T), 


60 


ELECTRICITY    AND    MATTER 


where  r  is  the  time  occupied  in  stopping  the 
particle;  outside  the  outer  sphere  the  configura- 
tion of  the  tubes  will  be  the  same  as  if  the  par- 
ticle had  not  been  stopped,  i.  e.,  the  tubes  will  be 
the  plane  at  the  distance  Vt  in  front  of  the  par- 
ticle, and  this  plane  will  touch  the  outer  sphere. 
Inside  the  inner  sphere  the  Faraday  tubes  will  be 
uniformly  distributed,  hence  to  preserve  continuity 
these  tubes  must  run  round  in  the  shell  to  join  the 
sphere  as  in  Fig.  14.  We  thus  have  in  this  case 

two  pulses,  one  a 
plane  pulse  propa- 
gated in  the  direc- 
tion in  which  the 
particle  was  mov- 
ing before  it  was 
stopped,  the  other  a 
'A'  spherical  pulse  trav- 
elling outward  in  all 
directions. 

The  preceding 
method  can  be  ap- 
plied to  the  case 
when  the  charged  particle,  instead  of  being 
stopped,  has  its  velocity  altered  in  any  way ;  thus, 
if  the  velocity  v  of  the  particle  instead  of  being 


PIG.  14. 


RONTGEN    RAYS    AND    LIGHT  gl 

reduced  to  zero  is  merely  diminished  by  A  v,  we 
can  show,  as  on  page  57,  that  it  will  give  rise  to 
a  pulse  in  which  the  magnetic  force  If  is  given  by 
the  equation 

TT      e&v  sin  0 
±±—-    ~s — , 
rt> 

and  the  tangential  electric  force  T  by 
m  _  e .  A  v  sin  9 

Now  the  thickness  8  of  the  pulse  is  the  space 
passed  over  by  a  wave  of  light  during  the  time  the 
velocity  of  the  particle  is  changing,  hence  if  8 1 
is  the  time  required  to  produce  the  change  A  v  in 
the  velocity  8  =  F"8 1,  hence  we  have 

TT_     e  At;  sin  9          ^  _     e    &v  sin  9 

VTt~T~  T*Zi  ~T~  ; 

A  7) 

but  TfT  is  equal  to  —  f,  where/  is  the  acceleration 

of  the  particle,  hence  we  have 

TT  _         0    /,  sin  0          ^  _          0     />  sin  9 
V*  ~~^~  V*J  ~~r~ ' 

These  equations  show  that  a  charged  particle 
whose  motion  is  being  accelerated  produces  a  pulse 
of  electric  and  magnetic  forces  in  which  the  forces 
vary  inversely  as  the  distance  from  the  particle. 

Thus,  if  a  charged  body  were  made  to  vibrate  in 


52  ELECTRICITY    AND    MATTER 

such  a  way  that  its  acceleration  went  through 
periodic  changes,  periodic  waves  of  electric  and 
magnetic  force  would  travel  out  from  the  charged 
body.  These  waves  would,  on  the  Electromag- 
netic Theory  of  Light,  be  light  waves,  provided 
the  periodic  changes  in  the  acceleration  of  the 
charged  body  took  place  with  sufficient  rapidity. 
The  method  we  have  been  investigating,  in  which 
we  consider  the  effect  produced  on  the  configura- 
tion of  the  Faraday  tubes  by  changes  in  the  mo- 
tion of  the  body,  affords  a  very  simple  way  of 
picturing  to  ourselves  the  processes  going  on  dur- 
ing the  propagation  of  a  wave  of  light  through 
the  ether.  We  have  regarded  these  as  arising 
from  the  propagation  of  transverse  tremors  along 
the  tightly  stretched  Faraday  tubes;  in  fact,  we 
are  led  to  take  the  same  view  of  the  propagation 
of  light  as  the  following  extracts  from  the  paper, 
"Thoughts  on  Ray  Vibrations,"  show  to  have 
been  taken  by  Faraday  himself.  Faraday  says, 
"  The  view  which  I  am  so  bold  to  put  forward 
considers  therefore  radiations  as  a  high  species  of 
vibration  in  the  lines  of  force  which  are  known 
to  connect  particles  and  also  masses  together." 

This  view  of  light  as  due  to  the  tremors  in 
tightly  stretched  Faraday  tubes  raises  a  question 


R'ONTGEN  RAYS  AND  LIGHT  53 

which  I  have  not  seen  noticed.  The  Faraday 
tubes  stretching  through  the  ether  cannot  be 
regarded  as  entirely  filling  it.  They  are  rather 
to  be  looked  upon  as  discrete  threads  embedded 
in  a  continuous  ether,  giving  to  the  latter  a  fibrous 
structure ;  but  if  this  is  the  case,  then  on  the  view 
we  have  taken  of  a  wave  of  light  the  wave  it- 
self must  have  a  structure,  and  the  front  of  the 
wave,  instead  of  being,  as  it  were,  uniformly  illu- 
minated, will  be  represented  by  a  series  of  bright 
specks  on  a  dark  ground,  the  bright  specks  cor- 
responding to  the  places  where  the  Faraday  tubes 
cut  the  wave  front. 

Such  a  view  of  the  constitution  of  a  light  wave 
would  explain  a  phenomenon  which  has  always 
struck  me  as  being  very  remarkable  and  difficult 
to  reconcile  with  the  view  that  a  light  wave,  or 
rather  in  this  case  a  Rontgen  ray,  does  not  possess 
a  structure.  We  have  seen  that  the  method  of 
propagation  and  constitution  of  a  Rontgen  ray 
is  the  same  as  in  a  light  wave,  so  that  any 
general  consideration  about  structure  in  Ront- 
gen rays  will  apply  also  to  light  waves.  The 
phenomenon  in  question  is  this:  Rontgen  rays 
are  able  to  pass  very  long  distances  through 
gases,  and  as  they  pass  through  the  gas  they 


64  ELECTRICITY   AND   MATTER 

ionize  it,  splitting  up  the  molecules  into  posi- 
tive and  negative  ions ;  the  number  of  molecules 
so  split  up  is,  however,  an  exceedingly  small  frac- 
tion, less  than  one-billionth,  even  for  strong  rays,  of 
the  number  of  molecules  in  the  gas.  Now,  if  the 
conditions  in  the  front  of  the  wave  are  uniform,  all 
the  molecules  of  the  gas  are  exposed  to  the  same 
conditions ;  how  is  it  then  that  so  small  a  propor- 
tion of  them  are  split  up  ?  It  might  be  argued  that 
those  split  up  are  in  some  special  condition — that 
they  possess,  for  example,  an  amount  of  kinetic 
energy  so  much  exceeding  the  average  kinetic 
energy  of  the  molecules  of  the  gas  that,  in  accord- 
ance with  Maxwell's  Law  of  Distribution  of 
Kinetic  energy,  their  number  would  be  exceedingly 
small  in  comparison  with  the  whole  number  of 
molecules  of  the  gas ;  but  if  this  were  the  case  the 
same  law  of  distribution  shows  that  the  number 
in  this  abnormal  condition  would  increase  very 
rapidly  with  the  temperature,  so  that  the  ioniza- 
tion  produced  by  the  Rontgen  rays  ought  to  in- 
crease very  rapidly  as  the  temperature  increases. 
Recent  experiments  made  by  Mr.  McClung  in  the 
Cavendish  Laboratory  show  that  no  appreciable 
increase  in  the  ionization  is  produced  by  raising 
the  temperature  of  a  gas  from  15°C.  to  200°  C., 


RONTGEN   RAYS   AND    LIGHT  55 

whereas  the  number  of  molecules  possessing  an 
abnormal  amount  of  kinetic  energy  would  be 
enormously  increased  by  this  rise  in  temperature. 
The  difficulty  in  explaining  the  small  ionization  is 
removed  if,  instead  of  supposing  the  front  of  the 
Rontgen  ray  to  be  uniform,  we  suppose  that  it  con- 
sists of  specks  of  great  intensity  separated  by 
considerable  intervals  where  the  intensity  is  very 
small,  for  in  this  case  all  the  molecules  in  the  field, 
and  probably  even  different  parts  of  the  same 
molecule,  are  not  exposed  to  the  same  conditions, 
and  the  case  becomes  analogous  to  a  swarm  of 
cathode  rays  passing  through  the  gas,  in  which 
case  the  number  of  molecules  which  get  into  col- 
lision with  the  rays  may  be  a  very  small  fraction 
of  the  whole  number  of  molecules. 

To  return,  however,  to  the  case  of  the  charged 
particle  whose  motion  is  accelerated,  we  have 
seen  that  from  the  particle  electric  and  magnetic 
forces  start  and  travel  out  radially  with  the  ve- 
locity of  light,  both  the  radial  and  magnetic  forces 
being  at  right  angles  to  the  direction  in  which 
they  are  travelling;  but  since  (see  page  25) 
each  unit  volume  of  the  electro-magnetic  field  has 
an  amount  of  momentum  equal  to  the  product  of 
the  density  of  the  Faraday  tube  and  the  magnetic 


QQ  ELECTRICITY   AND   MATTER 

force,  the  direction  of  the  momentum  being  at 
right  angles  to  both  these  quantities,  there  will  be 
the  wave  due  to  the  acceleration  of  the  charged 
particle,  and  indeed  in  any  electric  or  light  wave 
momentum  in  the  direction  of  propagation  of  the 
wave.  Thus,  if  any  such  wave,  for  example  a 
wave  of  light,  is  absorbed  by  the  substance  through 
which  it  is  passing,  the  momentum  in  the  wave 
will  be  communicated  to  the  absorbing  substance, 
which  will,  therefore,  experience  a  force  tending  to 
push  it  in  the  direction  the  light  is  travelling. 
Thus,  when  light  falls  normally  on  a  blackened  ab- 
sorbing substance,  it  will  repel  that  substance. 
This  repulsion  resulting  from  radiation  was  shown 
by  Maxwell  to  be  a  consequence  of  the  Electro- 
magnetic Theory  of  Light ;  it  has  lately  been  de- 
tected and  measured  by  Lebedew  by  some  most 
beautiful  experiments,  which  have  been  confirmed 
and  extended  by  Nichols  and  Hull. 

The  pressure  experienced  by  the  absorbing  sub- 
stance will  be  proportional  to  its  area,  while  the 
weight  of  the  substance  is  proportional  to  its  vol- 
ume. Thus,  if  we  halve  the  linear  dimensions  we 
reduce  the  weight  to  one-eighth  while  we  only  re- 
duce the  pressure  of  radiation  to  one-quarter ;  thus, 
by  sufficiently  reducing  the  size  of  the  absorbing 


RONTGEN   RAYS    AND   LIGHT  67 

body  we  must  arrive  at  a  stage  when  the  forces 
due  to  radiation  exceed  those  which,  like  weight, 
are  proportional  to  the  volume  of  the  substance. 
On  this  principle,  knowing  the  intensity  of  the 
radiation  from  the  sun,  Arrhenius  has  shown  that 
for  an  opaque  sphere  of  unit  density  10"6  cm.  in 
diameter  the  repulsion  due  to  the  radiation  from 
the  sun  would  just  balance  the  sun's  attraction, 
while  all  bodies  smaller  than  this  would  be  re- 
pelled from  the  sun,  and  he  has  applied  this  prin- 
ciple to  explain  the  phenomena  connected  with 
the  tails  of  comets.  Poynting-has  recently  shown 
that  if  two  spheres  of  unit  density  about  39  cm. 
in  diameter  are  at  the  temperature  of  27°  C.  and 
protected  from  all  external  radiation,  the  re- 
pulsion due  to  the  radiation  emitted  from  the 
spheres  will  overpower  their  gravitational  at- 
traction so  that  the  spheres  will  repel  each 
other. 

Again,  when  light  is  refracted  and  reflected 
at  a  transparent  surface,  the  course  of  the  light 
and  therefore  the  direction  of  momentum  is 
changed,  so  that  the  refracting  substance  must 
have  momentum  communicated  to  it.  It  is  easy 
to  show  that  even  when  the  incidence  of  the  light 
is  oblique  the  momentum  communicated  to  the 


gg  ELECTRICITY    AND   MATTER 

substance  is  normal  to  the  refracting  surface. 
There  are  many  interesting  problems  connected 
with  the  forces  experienced  by  refracting  prisms 
when  light  is  passing  through  them  which  will 
suggest  themselves  to  you  if  you  consider  the 
changes  in  momentum  experienced  by  the  light 
wave  in  its  course  through  the  prism.  Tangential 
forces  due  to  light  have  not,  so  far  as  I  know, 
been  detected  experimentally.  These,  however, 
must  exist  in  certain  cases ;  such,  for  example,  as 
when  light  incident  obliquely  is  imperfectly  re- 
flected from  a  metallic  surface. 

The  waves  of  electric  and  magnetic  force  which 
radiate  from  an  accelerated  charge  particle  carry 
energy  with  them.  This  energy  is  radiated  into 
space,  so  that  the  particle  is  constantly  losing  en- 
ergy. The  rate  at  which  energy  is  radiating  from 

1  e2f* 
the  particle  can  easily  be  shown  to  be  o —      where 

e  is  the  charge  on  the  particle,/  its  acceleration, 
and  V  the  velocity  of  light.  If  we  take  into  ac- 
count this  loss  of  energy  by  the  particle  when  its 
motion  is  being  accelerated,  we  find  some  interest- 
ing results.  Thus,  for  example,  if  a  particle  of 
mass  77i  and  charge  e  starting  from  rest  is  acted 
upon  by  a  constant  electric  force,  JT,  the  particle 


RO'NTGEN  RAYS  AND  LIGHT  69 

does  not  at  once  attain  the  acceleration  —-  as  it 

m 

would  if  there  were  no  loss  of  energy  by  radia- 
tion; on  the  contrary,  the  acceleration  of  the  parti- 
cle is  initially  zero,  and  it  is  not  until  after  the 

e2 
lapse  of  a  time  comparable  with  -y  —  that  the 

particle  acquires  even  an  appreciable  fraction  of 
its  final  acceleration.  Thus,  the  rate  at  which  the 


e2 


particle  loses  energy  is  during  the  time  -y  —  very 

small  compared  with  the  ultimate  rate.  Thus,  if 
the  particle  were  acted  on  by  a  wave  of  electric 

e* 
force  which  only  took  a  time  comparable  with  -y  — 

to  pass  over  the  particle,  the  amount  of  energy  ra- 
diated by  the  particle  would  be  a  very  much  smaller 
fraction  of  the  energy  in  the  wave  than  it  would  be 
if  the  particle  took  a  time  equal  to  a  considerable 

e2 
multiple  of  y-—  to  pass  over  the  particle.  This  has 

an  important  application  in  explaining  the  greater 
penetrating  power  of  "  hard  "  Kontgen  rays  than 
of  "  soft  "  ones.  The  "  hard  "  rays  correspond  to 
thin  pulses,  the  "  soft  "  ones  to  thick  ones  ;  so  that 
a  smaller  proportion  of  the  energy  in  the  "  hard  " 
rays  will  be  radiated  away  by  the  charged  particles 


70  ELECTRICITY    AND    MATTER  ^ 

over  which  they  pass  than  in  the  case  of  the  "soft" 
rays. 

By  applying  the  law  that  the  rate  at  which  en- 


ergy  is  radiating  is  equal  to  „  -T^-  to  the  case  of 

a  charged  particle  revolving  in  a  circular  orbit  un- 
der an  attractive  force  varying  inversely  as  the 
square  of  the  distance,  we  find  that  in  this  case 
the  rate  of  radiation  is  proportional  to  the  eighth 
power  of  the  velocity,  or  to  the  fourth  power  of 
the  energy.  Thus,  the  rate  of  loss  of  energy  by 
radiation  increases  very  much  more  rapidly  than 
the  energy  of  the  moving  body. 


CHAPTER  IV 

THE     ATOMIC    STRUCTURE    OF    ELECTRICITY 

HITHERTO  we  have  been  dealing  chiefly  with  the 
properties  of  the  lines  of  force,  with  their  ten- 
sion, the  mass  of  ether  they  carry  along  with  them, 
and  with  the  propagation  of  electric  disturbances 
along  them ;  in  this  chapter  we  shall  discuss  the 
nature  of  the  charges  of  electricity  which  form  the 
beginnings  and  ends  of  these  lines.  We  shall  show 
that  there  are  strong  reasons  for  supposing  that 
these  changes  have  what  may  be  called  an  atomic 
structure ;  any  charge  being  built  up  of  a  number 
of  finite  individual  charges,  all  equal  to  each  other : 
just  as  on  the  atomic  theory  of  matter  a  quantity 
of  hydrogen  is  built  up  of  a  number  of  small  par- 
ticles called  atoms,  all  the  atoms  being  equal  to 
each  other.  If  this  view  of  the  structure  of  elec- 
tricity is  correct,  each  extremity  of  a  Faraday  tube 
will  be  the  place  from  which  a  constant  fixed  num- 
ber of  tubes  start  or  at  which  they  arrive. 

Let  us  first  consider  the  evidence  given  by  the 
laws  of  the  electrolysis  of  liquids.  Faraday 


72  ELECTRICITY    AND   MATTER 

showed  that  when  electricity  passes  through  a 
liquid  electrolyte,  the  amount  of  negative  electric- 
ity given  up  to  the  positive  electrode,  and  of  posi- 
tive electricity  given  to  the  negative  electrode,  is 
proportional  to  the  number  of  atoms  coming  up 
to  the  electrode.  Let  us  first  consider  monovalent 
elements,  such  as  hydrogen,  chlorine,  sodium,  and 
so  on ;  he  showed  that  when  the  same  number  of 
atoms  of  these  substances  deliver  up  their 
charges  to  the  electrode,  the  quantity  of  electricity 
communicated  is  the  same  whether  the  carriers 
are  atoms  of  hydrogen,  chlorine,  or  sodium,  in- 
dicating that  each  atom  of  these  elements  carries 
the  same  charge  of  electricity.  Let  us  now  go  to 
the  divalent  elements.  We  find  again  that  the  ions 
of  all  divalent  elements  carry  the  same  charge, 
but  that  a  number  of  ions  of  the  divalent  ele- 
ment carry  twice  the  charge  carried  by  the  same 
number  of  ions  of  a  univalent  element,  showing 
that  each  ion  of  a  divalent  element  carries  twice 
as  much  charge  as  the  univalent  ion ;  again,  a  tri- 
valent  ion  carries  three  times  the  charge  of  a  uni- 
valent ion,  and  so  on.  Thus,  in  the  case  of  the  elec- 
trolysis of  solutions  the  charges  carried  by  the 
ions  are  either  the  charge  on  the  hydrogen  ion  or 
twice  that  charge,  or  three  times  the  charge,  and 


THE    ATOMIC    STRUCTURE   OF    ELECTRICITY        73 

so  on.  The  charges  we  meet  with  are  always  an 
integral  multiple  of  the  charge  carried  by  the  hy- 
drogen atom  ;  we  never  meet  with  fractional  parts 
of  this  charge.  This  very  remarkable  fact  shows, 
as  Helmholtz  said  in  the  Faraday  lecture,  that 
"  if  we  accept  the  hypothesis  that  the  elementary 
substances  are  composed  of  atoms,  we  cannot  avoid 
the  conclusion  that  electricity,  positive  as  well  as 
negative,  is  divided  into  definite  elementary  por- 
tions which  behave  like  atoms  of  electricity." 

When  we  consider  the  conduction  of  electricity 
through  gases,  the  evidence  in  favor  of  the  atomic 
character  of  electricity  is  even  stronger  than  it  is 
in  the  case  of  conduction  through  liquids,  chiefly 
because  we  know  more  about  the  passage  of  elec- 
tricity through  gases  than  through  liquids. 

Let  us  consider  for  a  moment  a  few  of  the  prop- 
erties of  gaseous  conduction.  When  a  gas  has 
been  put  into  the  conducting  state — say,  by  expos- 
ure to  Rontgen  rays — it  remains  in  this  state  for 
a  sufficiently  long  time  after  the  rays  have  ceased 
to  enable  us  to  study  its  properties.  We  find  that 
we  can  filter  the  conductivity  out  of  the  gas  by 
sending  the  gas  through  a  plug  of  cotton-wool,  or 
through  a  water-trap.  Thus,  the  conductivity  is 
due  to  something  mixed  with  the  gas  which  can 


74  ELECTRICITY   AND   MATTER 

be  filtered  out  of  it;  again,  the  conductivity  is 
taken  out  of  the  gas  when  it  is  sent  through  a 
strong  electric  field.  This  result  shows  that  the 
constituent  to  which  the  conductivity  of  the  gas  is 
due  consists  of  charged  particles,  the  conductivity 
arising  from  the  motion  of  these  particles  in  the 
electric  field.  We  have  at  the  Cavendish  Labora- 
tory measured  the  charge  of  electricity  carried  by 
those  particles. 

The  principle  of  the  method  first  used  is  as  fol- 
lows. If  at  any  time  there  are  in  the  gas  n  of  these 
particles  charged  positively  and  n  charged  nega- 
tively, and  if  each  of  these  carries  an  electric  charge 
e,  we  can  easily  by  electrical  methods  determine  n  e, 
the  quantity  of  electricity  of  our  sign  present  in 
the  gas.  One  method  by  which  this  can  be  done 
is  to  enclose  the  gas  between  two  parallel  metal 
plates,  one  of  which  is  insulated.  Now  suppose  we 
suddenly  charge  up  the  other  plate  positively  to  a 
very  high  potential,  this  plate  will  now  repel  the 
positive  particles  in  the  gas,  and  these  before  they 
have  time  to  combine  with  the  negative  particles 
will  be  driven  against  the  insulated  plate.  Thus, 
all  the  positive  charge  in  the  gas  will  be  driven 
against  the  insulated  plate,  where  it  can  be  meas- 
ured by  an  electrometer.  As  this  charge  is  equal 


THE   ATOMIC    STRUCTURE   OF   ELECTRICITY        75 

to  n  e  we  can  in  this  way  easily  determine  n  e :  if 
then  we  can  devise  a  means  of  measuring  n  we 
shall  be  able  to  find  e.  The  method  by  which  I 
determined  n  was  founded  on  the  discovery  by 
C.  T.  R  Wilson  that  the  charged  particles  act  as 
nuclei  round  which  small  drops  of  water  condense, 
when  the  particles  are  surrounded  by  damp  air 
cooled  below  the  saturation  point.  In  dust-free 
air,  as  Aitken  showed,  it  is  very  difficult  to  get  a 
fog  when  damp  air  is  cooled,  since  there  are  no 
nuclei  for  the  drops  to  condense  around ;  if  there 
are  charged  particles  in  the  dust-free  air,  however, 
a  fog  will  be  deposited  round  these  by  a  supersat- 
uration  far  less  than  that  required  to  produce  any 
appreciable  effect  when  no  charged  particles  are 
present. 

Thus,  in  sufficiently  supersaturated  damp  air  a 
cloud  is  deposited  on  these  charged  particles, 
and  they  are  thus  rendered  visible.  This  is  the 
first  step  toward  counting  them.  The  drops  are, 
however,  far  too  small  and  too  numerous  to  be 
counted  directly.  We  can,  however,  get  their 
number  indirectly  as  follows :  suppose  we  have  a 
number  of  these  particles  in  dust-free  air  in  a 
closed  vessel,  the  air  being  saturated  with  water 
vapor,  suppose  now  that  we  produce  a  sudden 


76  ELECTRICITY   AND   MATTER 

expansion  of  the  air  in  the  vessel;  this  will  cool 
the  air,  it  will  be  supersaturated  with  vapor,  and 
drops  will  be  deposited  round  the  charged  parti- 
cles. Now  if  we  know  the  amount  of  expansion 
produced  we  can  calculate  the  cooling  of  the  gas, 
and  therefore  the  amount  of  water  deposited. 
Thus,  we  know  the  volume  of  water  in  the  form  of 
drops,  so  that  if  we  know  the  volume  of  one  drop 
we  can  deduce  the  number  of  drops.  To  find  the 
size  of  a  drop  we  make  use  of  an  investigation 
by  Sir  George  Stokes  on  the  rate  at  which  small 
spheres  fall  through  the  air.  In  consequence  of 
the  viscosity  of  the  air  small  bodies  fall  exceedingly 
slowly,  and  the  smaller  they  are  the  slower  they 
fall.  Stokes  showed  that  if  a  is  the  radius  of  a 
drop  of  water,  the  velocity  v  with  which  it  falls 
through  the  air  is  given  by  the  equation 


-9M 

when  g  is  the  acceleration  due  to  gravity  =  981 
and  /A  the  coefficient  of  viscosity  of  air  =  .00018; 

thus 

^-1.21X106^2; 

hence  if  we  can  determine  v  we  can  determine 
the  radius  and  hence  the  volume  of  the  drop. 


THE    ATOMIC    STRUCTURE    OF   ELECTRICITY        77 

But  v  is  evidently  the  velocity  with  which  the 
cloud  round  the  charged  particle  settles  down,  and 
can  easily  be  measured  by  observing  the  move- 
ment  of  the  top  of  the  cloud.  In  this  way  I 
found  the  volume  of  the  drops,  and  thence  n  the 
number  of  particles.  As  n  e  had  been  determined 
by  electrical  measurements,  the  value  of  e  could 
be  deduced  when  n  was  known ;  in  this  way  I 
found  that  its  value  is 

3.4  X  10-10  Electrostatic  C.  G.  S.  units. 

Experiments  were  made  with  air,  hydrogen, 
and  carbonic  acid,  and  it  was  found  that  the 
ions  had  the  same  charge  in  all  these  gases ;  a 
strong  argument  in  favor  of  the  atomic  character 
of  electricity. 

We  can  compare  the  charge  on  the  gaseous  ion 
with  that  carried  by  the  hydrogen  ion  in  the  elec- 
trolysis of  solutions  in  the  following  way:  We 
know  that  the  passage  of  one  electro-magnetic 
unit  of  electric  charge,  or  3  X  1010  electrostatic 
units,  through  acidulated  water  liberates  1.23  c.c. 
of  hydrogen  at  the  temperature  15°C.  and  pressure 
of  one  atmosphere ;  if  there  are  JV  molecules  in  a 
c.c.  of  a  gas  at  this  temperature  and  pressure  the 
number  of  hydrogen  ions  in  1.23  c.c.  is  2.46  N, 


78  ELECTRICITY   AND   MATTER 

so  that  if  E  is  the  charge  on  the  hydrogen  ion  in 
the  electrolyis  of  solution, 

2.46  NJS=  3X  1010, 
or    E=  1.22  X  1010-f-JV; 

Now,  e,  the  charge  on  the  gas  ion  is  3.4X10'10, 
hence  if  ^V=  3.6  X1019  the  charge  on  the  gaseous 
ion  will  equal  the  charge  on  the  electrolytic  ion. 
Now,  in  the  kinetic  theory  of  gases  methods  are 
investigated  for  determining  this  quantity  IV,  or 
Avogadro's  Constant,  as  it  is  sometimes  called ;  the 
values  obtained  by  this  theory  vary  somewhat 
with  the  assumptions  made  as  to  the  nature  of 
the  molecule  and  the  nature  of  the  forces  which  one 
molecule  exerts  on  another  in  its  near  neighbor- 
hood. The  value  3.6 X1019  is>  however,  in  good 
agreement  with  some  of  the  best  of  these  deter- 
minations, and  hence  we  conclude  that  the  charge 
on  the  gaseous  ion  is  equal  to  the  charge  on  the 
electrolytic  ion. 

Dr.  H.  A.  Wilson,  of  the  Cavendish  Laboratory, 
by  quite  a  different  method,  obtained  practically 
the  same  value  for  e  as  that  given  above.  His 
method  was  founded  on  the  discovery  by  C.  T.  R. 
Wilson  that  it  requires  less  supersatiiration  to 
deposit  clouds  from  moist  air  on  negative  ions 


THE    ATOMIC    STRUCTURE    OF    ELECTRICITY        79 

than  it  does  on  positive.  Thus,  by  suitably 
choosing  the  supersaturation,  we  can  get  the 
cloud  deposited  on  the  negative  ions  alone,  so 
that  each  drop  in  the  cloud  is  negatively  charged ; 
by  observing  the  rate  at  which  the  cloud  falls  we 
can,  as  explained  above,  determine  the  weight  of 
each  drop.  Now,  suppose  we  place  above  the 
cloud  a  positively  electrified  plate,  the  plate  will 
attract  the  cloud,  and  we  can  adjust  the  charge  on 
the  plate  until  the  electric  attraction  just  balances 
the  weight  of  a  drop,  and  the  drops,  like  Mahomet's 
coffin,  hang  stationary  in  the  air;  if  X  is  the 
electric  force  then  the  electric  attraction  on  the 
drop  is  Xe,  when  e  is  the  charge  on  the  drop.  As 
X  e  is  equal  to  the  weight  of  the  drop  which  is 
known,  and  as  we  can  measure  X,  e  can  be  at  once 
determined. 

Townsend  showed  that  the  charge  on  the 
gaseous  ion  is  equal  to  that  on  the  ion  of  hydrogen 
in  ordinary  electrolysis,  by  measuring  the  coeffi- 
cient of  diffusion  of  the  gaseous  ions  and  com- 
paring it  with  the  velocity  acquired  by  the  ion 
under  a  given  electric  force.  Let  us  consider  the 
case  of  a  volume  of  ionized  gas  between  two 
horizontal  planes,  and  suppose  that  as  long  as  we 
keep  in  any  horizontal  layer  the  number  of  ions 


gO  ELECTRICITY   AND   MATTER 

remains  the  same,  but  that  the  number  varies  as 
we  pass  from  one  layer  to  another;  let  x  be  the 
distance  of  a  layer  from  the  lower  plane,  n 
the  number  of  ions  of  one  sign  in  unit  volume 
of  this  layer,  then  if  D  be  the  coefficient  of 
diffusion  of  the  ions,  the  number  of  ions  which 
in  one  second  pass  downward  through  unit  area 
of  the  layer  is 

dn 


so  that  the  average  velocity  of  the  particles  down- 
ward is 


n  dx 

The  force  which  sets  the  ions  in  motion  is  the 
variation  in  the  partial  pressure  due  to  the  ions  ;  if 
this  pressure  is  equal  top,  the  force  acting  on  the 

ions  in  a  unit  volume  is  -7—  >  and  the  average  force 

per  ion  is  -  -•?—.     Now  we   can  find  the  velocity 

which  an  ion  acquires  when  acted  upon  by  a 
known  force  by  measuring,  as  Rutherford  and 
Zeleny  have  done,  the  velocities  acquired  by  the 
ions  in  an  electric  field.  They  showed  that  this 
velocity  is  proportional  to  the  force  acting  on  the 
ion,  so  that  if  A  is  the  velocity  when  the  electric 


THE   ATOMIC    STRUCTURE   OF    ELECTRICITY        81 

force  is  JTand  when  the  force  acting  on  the  ion  is 
therefore  X  e,  the  velocity  for  unit  force  will  be 

-==r-,  and  the  velocity  when  the  force  is  -  -£.  will 
2L  e  n  ax 

therefore  be 


_ 

n  dx  Xe' 

this  velocity  we  have  seen,  however,  to  be  equal  to 

D_  dn. 

n  dx' 
hence  we  have 


—  =  D  d—  .  (I) 

dx  Xe  dx  ' 

Now  if  the  ions  behave  like  a  perfect  gas,  the 
pressure  p  bears  a  constant  ratio  to  n,  the  number 
of  ions  per  unit  volume.  This  ratio  is  the  same 
for  all  gases,  at  the  same  temperature,  so  that  if 
N  is  Avogadro's  constant,  i.e.,  the  number  of  mol- 
ecules in  a  cubic  centimetre  of  gas  at  the  atmos- 
pheric pressure  P 

p  _      n 
p-~-N> 
and  equation  (1)  gives  us 

PA       ,- 

=Ne. 


Thus,  by  knowing  D  and  a  we  can  find  the  value 
of  Ne.   In  this  way  Townsend  found  that  Ne  was 


82  ELECTRICITY   AND   MATTER 

the  same  in  air,  hydrogen,  oxygen,  and  carbonic 
acid,  and  the  mean  of  his  values  was  N  e  —  1.24 
X  1010.  We  have  seen  that  if  E\&  the  charge  on 
the  hydrogen  ion 

NE  =  1.22  X  1010. 

Thus,  these  experiments  show  that  e=E,  or  that 
the  charge  on  the  gaseous  ion  is  equal  to  the 
charge  carried  by  the  hydrogen  ion  in  the  elec- 
trolysis of  solutions. 

The  equality  of  these  charges  has  also  been 
proved  in  a  very  simple  way  by  H.  A.  Wilson, 
who  introduced  per  second  into  a  volume  of  air 
at  a  very  high  temperature,  a  measured  quan- 
tity of  the  vapor  of  metallic  salts.  This  vapor 
got  ionized  and  the  mixture  of  air  and  vapor  ac- 
quired very  considerable  conductivity.  The  cur- 
'rent  through  the  vapor  increased  at  first  with  the 
electromotive  force  used  to  drive  it  through  the 
gas,  but  this  increase  did  not  go  on  indefinitely, 
for  after  the  current  had  reached  a  certain  value 
no  further  increase  in  the  electromotive  force  pro- 
duced any  change  in  the  current.  The  current,  as 
in  all  cases  of  conduction  through  gases,  attained 
a  maximum  value  called  the  "  saturation  current," 
which  was  not  exceeded  until  the  electric  field  ap- 
plied to  the  gas  approached  the  intensity  at  which 


s         5  *  * 

THE    ATOMIC    STRUCTURE'  OF  'ELECTRICITY        33 

sparks  began  to  pass  through  the  gas.  Wilson 
found  that  the  saturation  current  through  the  salt 
vapor  was  just  equal  to  the  current  which  if  it 
passed  through  an  aqueous  solution  of  the  salt 
would  electrolyse  in  one  second  the  same  amount 
of  salt  as  was  fed  per  second  into  the  hot  air. 

It  is  worth  pointing  out  that  this  result  gives 
us  a  method  of  determining  Avogadro's  Constant 
which  is  independent  of  any  hypothesis  as  to  the 
shape  or  size  of  molecules,  or  of  the  way  in  which 
they  act  upon  each  other.  If  N\&  this  constant,  e 
the  charge  on  an  ion,  then  N  e  =  1.22  X  1010  and 
we  have  seen  that  e  —  3.4  X  1010,  so  that  N=  3.9 
X  1019.  fo~*] 

Thus,  whether  we  study  the  conduction  of  elec- 
tricity through  liquids  or  through  gases,  we  are 
led  to  the  conception  of  a  natural  unit  or  atom  of 
electricity  of  which  all  charges  are  integral  mul- 
tiples, just  as  the  mass  of  a  quantity  of  hydro- 
gen is  an  integral  multiple  of  the  mass  of  a 
hydrogen  atom. 

Mass  of  the  Carriers  of  Electricity 

We  must  now  pass  on  to  consider  the  nature 
of  the  systems  which  carry  the  charges,  and  in 
order  to  have  the  conditions  as  simple  as  possible 


34  ELECTRICITY    AND    MATTER 

let  us  begin  with  the  case  of  a  gas  at  a  very  low 
pressure,  where  the  motion  of  the  particles  is  not 
impeded  by  collisions  with  the  molecules  of  the 
gas.  Let  us  suppose  that  we  have  a  particle  of 
mass  m,  carrying  a  charge  £,  moving  in  the  plane 
of  the  paper,  and  that  it  is  acted  on  by  a  uniform 
magnetic  field  at  right  angles  to  this  plane.  We 
have  seen  that  under  these  circumstances  the  par- 
ticle will  be  acted  upon  by  a  mechanical  force 
equal  toffe  v,  where  If  is  the  magnetic  force  and 
v  the  velocity  of  the  particle.  The  direction  of 
this  force  is  in  the  plane  of  the  paper  at  right 
angles  to  the  path  of  the  particle.  Since  the 
force  is  always  at  right  angles  to  the  direction 
of  motion  of  the  particle,  the  velocity  of  the  par- 
ticle and  therefore  the  magnitude  of  the  force  act- 
ing upon  it  will  not  alter,  so  that  the  path  of  the 
particle  will  be  that  described  by  a  body  acted 
upon  by  a  constant  normal  force.  It  is  easy  to  show 
that  this  path  is  a  circle  whose  radius  a  is  given 
by  the  equation 


mv  ,  v 

a  —  — rr-  V1) 


The  velocity  v  of  the  particle  may  be  deter- 
mined by  the  following  method  :  Suppose  the  par- 
ticle is  moving  horizontally  in  the  plane  of  the 


THE  ATOMIC  STRUCTURE  OF  ELECTRICITY    §5 

paper,  through  a  uniform  magnetic  field  H,  at 
light  angles  to  this  plane,  the  particle  will  be 
acted  upon  by  a  vertical  force  equal  to  H  e  v.  Now, 
if  in  addition  to  the  magnetic  force  we  apply  a 
vertical  electric  force  X,  this  will  exert  a  verti- 
cal mechanical  force  X  e  on  the  moving  particle. 
Let  us  arrange  the  direction  of  JTso  that  this  force 
is  in  the  opposite  direction  to  that  due  to  the  mag- 
net, and  adjust  the  value  of  X  until  the  two  forces 
are  equal.  We  can  tell  when  this  adjustment  has 
been  made,  since  in  this  case  the  motion  of  the 
particle  under  the  action  of  the  electric  and  mag- 
netic forces  will  be  the  same  as  when  both  these 
forces  are  absent.  When  the  two  forces  are  equal 
we  have 

X  e  =  If  e  v,      or 


Hence  if  we  have  methods  of  tracing  the  motion 
of  the  particle,  we  can  measure  the  radius  a  of  the 
circle  into  which  it  is  bent  by  a  constant  magnetic 
force,  and  determine  the  value  of  the  electric  force 
required  to  counteract  the  effect  of  the  magnetic 
force.  Equations  (1)  and  (2)  then  give  us  the 

means  of  finding  both  v  and  —  • 

0  772, 


g6  ELECTRICITY   AND   MATTER 

Values  of  -  -  for  Negatively  Electrified  Particles 
ftTL 

in  Gases  at  Low  Pressures 

The   value  of    -  has  been  determined  in  this 
m 

way  for  the  negatively  electrified  particles  which 
form  the  cathode  rays  which  are  so  conspicuous  a 
part  of  the  electric  discharge  through  a  gas  at  low 
pressures ;  and  also  for  the  negatively  electrified 
particles  emitted  by  metals,  (1)  when  exposed  to 
ultra-violet  light,  (2)  when  raised  to  the  tempera- 
ture of  incandescence.  These  experiments  have 

led  to  the  very  remarkable  result  that  the  value  of 
& 

—  is  the  same  whatever  the  nature  of  the  gas  in 
m 

which  the  particle  may  be  found,  or  whatever  the 
nature  of  the  metal  from  which  it  may  be  sup- 
posed to  have  proceeded.  In  fact,  in  every  case 

/? 

in  which  the  value  of  --  has  been  determined  for 
m 

negatively  electrified  particles  moving  with  veloci- 
ties considerably  less  than  the  velocity  of  light,  it 
has  been  found  to  have  the  constant  value  about 
10T,  the  units  being  the  centimetre,  gram,  and 

second,  and  the  charge  being  measured  in  electro- 

^ 
magnetic  units.  As  the  value  of  —  for  the  hydro- 


THE    ATOMIC    STRUCTURE    OF    ELECTRICITY        37 

gen  ion  in  the  electrolysis  of  liquids  is  only  104, 
and  as  we  have  seen  the  charge  on  the  gaseous 
ion  is  equal  to  that  on  the  hydrogen  ion  in  ordi- 
nary electrolysis,  we  see  that  the  mass  of  a  carrier 
of  the  negative  charge  must  be  only  about  one- 
thousandth  part  of  the  mass  of  hydrogen  atom ; 
the  mass  was  for  a  long  time  regarded  as  the  small- 
est mass  able  to  have  an  independent  existence. 

I  have  proposed  the  name  corpuscle  for  these 
units  of  negative  electricity.  These  corpuscles 
are  the  same  however  the  electrification  may  have 
arisen  or  wherever  they  may  be  found.  Negative 
electricity,  in  a  gas  at  a  low  pressure,  has  thus  a 
structure  analogous  to  that  of  a  gas,  the  corpuscles 
taking  the  place  of  the  molecules.  The  "  negative 
electric  fluid,"  to  use  the  old  notation,  resembles 
a  gaseous  fluid  with  a  corpuscular  instead  of  a 
molecular  structure. 

Carriers  of  Positive  Electrification 
We  can  apply  the  same  methods  to  determine 

/J 

the  values  of  —  for  the  carriers  of  positive  electri- 
m 

fication.  This  has  been  done  by  Wien  for  the 
positive  electrification  found  in  certain  parts  of 
the  discharge  in  a  vacuum  tube,  and  I  have 


gg  ELECTRICITY   AND   MATTER 

^ 

measured  —  for  the  positive  electrification  given 

off  by  a  hot  wire.  The  results  of  these  measure- 
ments form  a  great  contrast  to  those  for  the  nega- 
tive electrification,  for  —  for  the  positive  charge, 

instead  of  having,  as  it  has  for  the  negative,  the 
constant  high  value  107,  is  found  never  to  have  a 
value  greater  than  104,  the  value  it  would  have  if 

the  carrier  were  the  atom  of  hydrogen.     In  many 
/} 

cases  the  value  of  —  is  very  much  less  than  104,  m- 
wi 

dicating  that  in  these  cases  the  positive  charge  is 

carried  by  atoms  having  a  greater  mass  than  that 

g 
of  the  hydrogen  atom.  The  value  of --  varies  with 

TTL 

the  nature  of  the  electrodes  and  with  the  gas  in 
the  discharge  tube,  just  as  it  would  if  the  carriers 
of  the  positive  charge  were  the  atoms  of  the 
elements  which  happened  to  be  present  when  the 
positive  electrification  was  produced. 

These  results  lead  us  to  a  view  of  electrification 
which  has  a  striking  resemblance  to  that  of 
Franklin's  "One  Fluid  Theory  of  Electricity." 
Instead  of  taking,  as  Franklin  did,  the  electric 
fluid  to  be  positive  electricity  we  take  it  to  be 
negative.  The  "electric  fluid"  of  Franklin  cor- 


THE  ATOMIC  STRUCTURE  OF  ELECTRICITY    gg 

responds  to  an  assemblage  of  corpuscles,  negative 
electrification  being  a  collection  of  these  corpus- 
cles. The  transference  of  electrification  from  one 
place  to  another  is  effected  by  the  motion  of  cor- 
puscles from  the  place  where  is  a  gain  of  positive 
electrification  to  the  place  where  there  is  a  gain 
of  negative.  A  positively  electrified  body  is  one 
that  has  lost  some  of  its  corpuscles.  We  have 
seen  that  the  mass  and  charge  of  the  corpuscles 
have  been  determined  directly  by  experiment.  We 
in  fact  know  more  about  the  "  electric  fluid  "  than 
we  know  about  such  fluids  as  air  or  water. 


CHAPTER  V 

CONSTITUTION  OF  THE  ATOM 

WE  have  seen  that  whether  we  produce  the 
corpuscles  by  cathode  rays,  by  ultra-violet  light,  or 
from  incandescent  metals,  and  whatever  may  be 
the  metals  or  gases  present  we  always  get  the  same 
kind  of  corpuscles.  Since  corpuscles  similar  in  all 
respects  may  be  obtained  from  very  different  agents 
and  materials,  and  since  the  mass  of  the  corpuscles 
is  less  than  that  of  any  known  atom,  we  see  that 
the  corpuscle  must  be  a  constituent  of  the  atom  of 
many  different  substances.  That  in  fact  the  atoms 
of  these  substances  have  something  in  common. 

We  are  thus  confronted  with  the  idea  that  the 
atoms  of  the  chemical  elements  are  built  up  of  sim- 
pler systems ;  an  idea  which  in  various  forms  has 
been  advanced  by  more  than  one  chemist.  Thus 
Prout,  in  1815,  put  forward  the  view  that  the 
atoms  of  all  the  chemical  elements  are  built  up  of 
atoms  of  hydrogen ;  if  this  were  so  the  combining 
weights  of  all  the  elements  would,  on  the  assump- 


CONSTITUTION   OF   THE   ATOM  gi 

tion  that  there  was  no  loss  of  weight  when  the 
atoms  of  hydrogen  combined  to  form  the  atom  of 
some  other  element,  be  integers ;  a  result  not  in  ac- 
cordance with  observation.  To  avoid  this  discrep- 
ancy Dumas  suggested  that  the  primordial  atom 
might  not  be  the  hydrogen  atom,  but  a  smaller 
atom  having  only  one-half  or  one-quarter  of  the 
mass  of  the  hydrogen  atom.  Further  support  was 
given  to  the  idea  of  the  complex  nature  of  the 
atom  by  the  discovery  by  Newlands  and  Mende- 
leeff  of  what  is  known  as  the  periodic  law,  which 
shows  that  there  is  a  periodicity  in  the  properties 
of  the  elements  when  they  are  arranged  in  the  or- 
der of  increasing  atomic  weights.  The  simple  rela- 
tions which  exist  between  the  combining  weights 
of  several  of  the  elements  having  similar  chemical 
properties,  for  example,  the  fact  that  the  combin- 
ing weight  of  sodium  is  the  arithmetic  mean  of 
those  of  lithium  and  potassium,  all  point  to  the 
conclusion  that  the  atoms  of  the  different  elements 
have  something  in  common.  Further  evidence  in 
the  same  direction  is  afforded  by  the  similarity  in 
the  structure  of  the  spectra  of  elements  in  the  same 
group  in  the  periodic  series,  a  similarity  which  re- 
cent work  on  the  existence  in  spectra  of  series  of 
lines  whose  frequencies  are  connected  by  definite 


92  ELECTRICITY   AND   MATTER 

numerical  relations  has  done  much  to  emphasize 
and  establish ;  indeed  spectroscopic  evidence  alone 
has  led  Sir  Norman  Lockyer  for  a  long  time  to 
advocate  the  view  that  the  elements  are  really 
compounds  which  can  be  dissociated  when  the 
circumstances  are  suitable.  The  phenomenon  of 
radio-activity,  of  which  I  shall  have  to  speak  later, 
carries  the  argument  still  further,  for  there  seems 
good  reasons  for  believing  that  radio-activity  is 
due  to  changes  going  on  within  the  atoms  of  the 
radio-active  substances.  If  this  is  so  then  we 
must  face  the  problem  of  the  constitution  of  the 
atom,  and  see  if  we  can  imagine  a  model  which 
has  in  it  the  potentiality  of  explaining  the  re- 
markable properties  shown  by  radio-active  sub- 
stances. It  may  thus  not  be  superfluous  to  con- 
sider the  bearing  of  the  existence  of  corpuscles  on 
the  problem  of  the  constitution  of  the  atom;  and 
although  the  model  of  the  atom  to  which  we  are 
led  by  these  considerations  is  very  crude  and  im- 
perfect, it  may  perhaps  be  of  service  by  suggesting 
lines  of  investigations  likely  to  furnish  us  with  fur- 
ther information  about  the  constitution  of  the 
atom. 


CONSTITUTION    OF   THE    ATOM  93 

The  Nature  of  the  Unit  from  which  the  Atoms 
are  Built  Up 

Starting  from  the  hypothesis  that  the  atom 
is  an  aggregation  of  a  number  of  simpler  systems, 
let  us  consider  what  is  the  nature  of  one  of 
these  systems.  We  have  seen  that  the  cor- 
puscle, whose  mass  is  so  much  less  than  that  of  the 
atom,  is  a  constituent  of  the  atom,  it  is  natural  to 
regard  the  corpuscle  as  a  constituent  of  the  primor- 
dial system.  The  corpuscle,  however,  carries  a 
definite  charge  of  negative  electricity,  and  since 
with  any  charge  of  electricity  we  always  associate 
an  equal  charge  of  the  opposite  kind,  we  should 
expect  the  negative  charge  on  the  corpuscle  to  be 
associated  with  an  equal  charge  of  positive  electri- 
city. Let  us  then  take  as  our  primordial  system  an 
electrical  doublet,  with  a  negative  corpuscle  at  one 
end  and  an  equal  positive  charge  at  the  other,  the 
two  ends  being  connected  by  lines  of  electric  force 
which  we  suppose  to  have  a  material  existence. 
For  reasons  which  will  appear  later  on,  we  shall 
suppose  that  the  volume  over  which  the  positive 
electricity  is  spread  is  very  much  larger  than  the 
volume  of  the  corpuscle.  The  lines  of  force  will 
therefore  be  very  much  more  condensed  near  the 


94  ELECTRICITY    AND    MATTER 

corpuscle  than  at  any  other  part  of  the  system,  and 
therefore  the  quantity  of  ether  bound  by  the  lines 
of  force,  the  mass  of  which  we  regard  as  the  mass 
of  the  system,  will  be  very  much  greater  near  the 
corpuscle  than  elsewhere.  If,  as  we  have  sup- 
posed, the  size  of  the  corpuscle  is  very  small  com- 
pared with  the  size  of  the  volume  occupied  by  the 
positive  electrification,  the  mass  of  the  system  will 
practically  arise  from  the  mass  of  bound  ether 
close  to  the  corpuscle ;  thus  the  mass  of  the  sys- 
tem will  be  practically  independent  of  the  position 
of  its  positive  end,  and  will  be  very  approximately 
the  mass  of  the  corpuscles  if  alone  in  the  field. 
This  mass  (see  page  21)  is  for  each  corpuscle 

equal  to  — ,  where  e  is  the  charge  on  the  corpuscle 

ott 

and  a  its  radius — a,  as  we  have  seen,  being  about 
10-13  cm. 

Now  suppose  we  had  a  universe  consisting  of 
an  immense  number  of  these  electrical  doublets, 
which  we  regard  as  our  primordial  system  ;  if  these 
were  at  rest  their  mutual  attraction  would  draw 
them  together,  just  as  the  attractions  of  a  lot  of 
little  magnets  would  draw  them  together  if  they 
were  free  to  move,  and  aggregations  of  more  than 
one  system  would  be  formed. 


CONSTITUTION    OF   THE    ATOM  95 

If,  however,  the  individual  systems  were  orig- 
inally moving  with  considerable  velocities,  the  rel- 
ative velocity  of  two  systems,  when  they  came 
near  enough  to  exercise  appreciable  attraction  on 
each  other,  might  be  sufficient  to  carry  the  sys- 
tems apart  in  spite  of  their  mutual  attraction.  In 
this  case  the  formation  of  aggregates  would  be 
postponed,  until  the  kinetic  energy  of  the  units 
had  fallen  so  low  that  when  they  came  into 
collision,  the  tendency  to  separate  due  to  their 
relative  motion  was  not  sufficient  to  prevent  them 
remaining  together  under  their  mutual  attraction. 

Let  us  consider  for  a  moment  the  way  in  which 
the  kinetic  energy  of  such  an  assemblage  of  units 
would  diminish.  We  have  seen  (p.  68)  that  when- 
ever the  velocity  of  a  charged  body  is  changing 
the  body  is  losing  energy,  since  it  generates 
electrical  waves  which  radiate  through  space,  car- 
rying energy  with  them.  Thus,  whenever  the 
units  come  into  collision,  i.e.,  whenever  they 
come  so  close  together  that  they  sensibly  acceler- 
ate or  retard  each  other's  motion,  energy  will  be 
radiated  away,  the  whole  of  which  will  not  be 
absorbed  by  the  surrounding  units.  There  will 
thus  be  a  steady  loss  of  kinetic  energy,  and  after 
a  time,  although  it  may  be  a  very  long  time,  the 


96  ELECTRICITY   AND   MATTER 

kinetic  energy  will  fall  to  the  value  at  which  aggre- 
gation of  the  units  into  groups  of  two  will  begin ; 
these  will  later  on  be  followed  by  the  formation 
of  aggregates  containing  a  larger  number  of  units. 
In  considering  the  question  of  the  further  ag- 
gregation of  these  complex  groups,  we  must  re- 
member that  the  possibility  of  aggregation  will 
depend  not  merely  upon  the  velocity  of  the  aggre- 
gate as  a  whole,  i.e.,  upon  the  velocity  of  the 
centre  of  gravity,  but  also  upon  the  relative  ve- 
locities of  the  corpuscles  within  the  aggregate. 

Let  us  picture  to  ourselves  the  aggregate  as,  like 
the  ^Epinus  atom  of  Lord  Kelvin,  consisting  of  a 
sphere  of  uniform  positive  electrification,  and  ex- 
erting therefore  a  radial  electric  force  proportional 
at  an  internal  point  to  the  distance  from  the  centre, 
and  that  the  very  much  smaller  negatively  electri- 
fied corpuscles  are  moving  about 
inside  it.     The  number  of  corpus- 
cles is  the  number  of  units  which 
had  gone  to  make  up  the  aggre- 
gate, and  the  total  negative  elec- 
trification  on   the    corpuscles   is 
equal   to  the  positive  electrifica- 
tion on  the  sphere.     To  fix  our  ideas  let  us  take 
the  case  shown  in  Fig.  15  of  three  corpuscles 


CONSTITUTION    OF    THE    ATOM  97 

A,  J3,  <?,  arranged  within  the  sphere  at  the  corners 
of  an  equilateral  triangle,  the  centre  of  the  triangle 
coinciding  with  the  centre  of  the  sphere.  First 
suppose  the  corpuscles  are  at  rest ;  they  will  be  in 
equilibrium  when  they  are  at  such  a  distance 
from  the  centre  of  the  sphere  that  the  repulsion 
between  the  corpuscles,  which  will  evidently  be 
radial,  just  balances  the  radial  attraction  excited 
on  the  corpuscles  by  the  positive  electrification  of 
the  sphere.  A  simple  calculation  shows  that  this 
will  be  the  case  when  the  distance  of  the  corpuscle 
from  the  centre  is  equal  to  .57  times  the  radius  of 
the  sphere.  Next  suppose  that  the  corpuscles,  in- 
stead of  being  at  rest,  are  describing  circular  orbits 
round  the  centre  of  the  sphere.  Their  centrifugal 
force  will  carry  them  farther  away  from  the  centre 
by  an  amount  depending  upon  the  speed  with 
which  they  are  rotating  in  their  orbits.  As  we 
increase  this  speed  the  distance  of  the  corpuscles 
from  the  centre  of  the  sphere  will  increase  until 
at  a  certain  speed  the  corpuscles  will  reach  the 
surface  of  the  sphere ;  further  increases  in  speed 
will  cause  them  first  to  rotate  outside  the  sphere 
and  finally  leave  the  sphere  altogether,  when  the 
atom  will  break  up. 

In  this  way  we  see  that  the  constitution  of  the 


gg  ELECTRICITY   AND   MATTER 

aggregate  will  not  be  permanent,  if  the  kinetic 
energy  due  to  the  velocity  of  the  corpuscles  inside 
the  sphere  relative  to  the  centre  of  the  sphere  ex- 
ceeds a  certain  value.  We  shall,  for  the  sake  of 
brevity,  speak  of  this  kinetic  energy  of  the  cor- 
puscles within  the  atom  as  the  corpuscular  tem- 
perature of  the  atom,  and  we  may  express  the 
preceding  result  by  saying  that  the  atom  will  not 
be  stable  unless  its  corpuscular  temperature  is 
below  a  certain  value. 

We  must  be  careful  to  distinguish  between  cor- 
puscular temperature,  which  is  the  mean  kinetic 
energy  of  the  corpuscles  inside  the  atom,  and  the 
molecular  temperature,  which  is  the  mean  kinetic 
energy  due  to  the  motion  of  the  centre  of  gravity 
of  the  atom.  These  temperatures  are  probably  not 
in  any  very  close  relationship  with  each  other. 
They  would  be  proportional  to  each  other  if  the  law 
known  as  the  law  of  equipartition  of  energy  among 
the  various  degrees  of  freedom  of  the  atom  were  to 
apply.  This  law  is,  however,  inconsistent  with  the 
physical  properties  of  gases,  and  in  the  proof  given 
of  it  in  the  kinetic  theory  of  gases,  no  estimate  is 
given  of  the  time  required  to  establish  the  state  con- 
templated by  the  law ;  it  may  be  that  this  time  is  so 
long  that  gases  are  never  able  to  get  into  this  state. 


CONSTITUTION    OF    THE    ATOM  99 

Let  us  now  take  the  case  of  two  aggregations, 
A  and  JB,  whose  corpuscular  temperatures  are  high, 
though  not  so  high,  of  course,  as  to  make  A  and  B 
unstable  when  apart,  and  suppose,  in  order  to  give 
them  the  best  possible  chance  of  combining,  that 
the  centres  of  gravity  of  A  and  B  when  quite 
close  to  each  other  are  at  rest,  will  A  and  B 
unite  to  form  a  more  complex  aggregate  as  they 
would  if  the  corpuscles  in  them  were  at  rest  ?  We 
can  easily,  I  think,  see  that  they  will  not  necessa- 
rily do  so.  For  as  A  and  B  approach  each  other, 
under  their  mutual  attractions,  the  potential  en- 
ergy due  to  the  separation  of  A  and  B  will  dimin- 
ish and  their  kinetic  energy  will  increase.  This  in- 
crease in  the  kinetic  energy  of  the  corpuscles  in  A 
and  B  will  increase  the  tendency  of  the  corpuscles 
to  leave  their  atoms,  and  if  the  increase  in  the  kin- 
etic energy  is  considerable  A  and  B  may  each  lose 
one  or  more  corpuscles.  The  departure  of  a  cor- 
puscle will  leave  A  and  B  positively  charged, 
and  they  will  tend  to  separate  under  the  repulsion 
of  these  charges.  When  separated  they  will  have 
each  a  positive  charge ;  but  as  there  are  now  free 
corpuscles  with  negative  charges  moving  about  in 
the  region  in  which  A  and  B  are  situated,  these 
positive  charges  will  ultimately  be  neutralized  by 


100  ELECTRICITY    AND   MATTER 

corpuscles  striking  against  A  and  B  and  remain- 
ing in  combination  with  them. 

We  thus  conclude  that  unless  the  corpuscular 
temperature  after  union  is  less  than  a  certain  limit- 
ing value,  the  union  cannot  be  permanent,  the 
complex  formed  being  unstable,  and  incapable  of 
a  permanent  existence.  Now,  the  corpuscular 
temperature  of  the  aggregate  formed  by  A  and  B 
will  depend  upon  the  corpuscular  temperatures  of 
A  and  B  before  union,  and  also  upon  the  diminu- 
tion in  the  potential  energy  of  the  system  occa- 
sioned by  the  union  of  A  and  B.  If  the  corpuscu- 
lar temperatures  of  A  and  B  before  union  were 
very  high,  the  corpuscular  temperature  after  union 
would  be  high  also;  if  they  were  above  a  cer- 
tain limit,  the  corpuscular  temperature  after  union 
would  be  too  high  for  stability,  and  the  aggre- 
gate AB  would  not  be  formed.  Thus,  one  con- 
dition for  the  formation  of  complex  aggregates  is 
that  the  corpuscular  temperature  of  their  constitu- 
ents before  combination  should  be  sufficiently  low. 

If  the  moleculcw*  temperature  of  the  gas  in 
which  A  and  B  are  molecules  is  very  high,  com- 
bination may  be  prevented  by  the  high  relative 
velocity  of  A  and  B  carrying  them  apart  in  spite 
of  their  mutual  attraction.  The  point,  however, 


CONSTITUTION   OF   THE    ATOM 

which  I  wish  to  emphasize  is,  that  we  cannot  se- 
cure the  union  merely  by  lowering  the  molecular 
temperature,  i.e.,  by  cooling  the  gas  ;  union  will 
be  impossible  unless  the  corpuscular  temperature, 
i.e.,  the  kinetic  energy  due  to  the  motion  of  the 
corpuscles  inside  the  atom,  is  reduced  below  a  cer- 
tain value.  We  may  prevent  union  by  raising  the 
molecular  temperature  of  a  gas,  but  we  cannot  en- 
sure union  by  lowering  it. 

Thus,  to  take  a  specific  example,  the  reason,  on 
this  view,  why  the  atoms  of  hydrogen  present  on 
the  earth  do  not  combine  to  form  some  other  ele- 
ment, even  at  the  exceedingly  low  temperature  at 
which  hydrogen  becomes  liquid,  is  that  even  at 
this  temperature  the  kinetic  energy  of  the  corpus- 
cles inside  the  atom,  i.e.,  the  corpuscular  tempera- 
ture, is  too  great.  It  may  be  useful  to  repeat  here 
what  we  stated  before,  that  there  is  no  very  inti- 
mate connection  between  the  corpuscular  and  mo- 
lecular temperatures,  and  that  we  may  reduce  the 
latter  almost  to  the  absolute  zero  without  greatly 
affecting  the  former. 

We  shall  now  proceed  to  discuss  the  bearing  of 
these  results  on  the  theory  that  the  different 
chemical  elements  have  been  gradually  evolved  by 
the  aggregation  of  primordial  units. 


102  ELECTRICITY   AND   MATTER 

Let  us  suppose  that  the  first  stage  has  been 
reached  and  that  we  have  a  number  of  systems 
formed  by  the  union  of  two  units.  When  first 
these  binary  systems,  as  we  shall  call  them,  were 
formed,  the  corpuscles  in  the  system  would  have 
a  considerable  amount  of  kinetic  energy.  This 
would  be  so,  because  when  the  two  units  have 
come  together  there  must  be  an  amount  of  kinetic 
energy  produced  equal  to  the  diminution  in  the 
potential  energy  consequent  upon  the  coalescence  of 
the  two  units.  As  these  binary  systems  have  or- 
iginally high  corpuscular  temperatures  they  will 
not  be  likely  to  combine  with  each  other  or  with 
another  unit ;  before  they  can  do  so  the  kinetic 
energy  of  the  corpuscles  must  get  reduced. 

We  shall  proceed  immediately  to  discuss  the 
way  in  which  this  reduction  is  effected,  but  we 
shall  anticipate  the  result  of  the  discussion  by 
saying  that  it  leads  to  the  result  that  the  rate  of 
decay  in  the  corpuscular  temperature  probably 
varies  greatly  from  one  binary  system  to  another. 

Some  of  the  systems  will  therefore  probably 
have  reached  a  condition  in  which  they  are  able 
to  combine  with  each  other  or  with  a  single  unit 
long  before  others  are  able  to  do  so.  The  systems 
of  the  first  kind  will  combine,  and  thus  we  shall 


CONSTITUTION    OP   THE    ATOM  103 

have  systems  formed,  some  of  which  contain  three, 
others  four  units,  while  at  the  same  time  there  are 
many  of  the  binary  systems  left.  Thus,  the  appear- 
ance of  the  more  complex  systems  need  not  be 
simultaneous  with  the  disappearance  of  all  the  sim- 
pler ones. 

The  same  principle  will  apply  to  the  formation 
of  further  aggregations  by  the  systems  containing 
three  or  four  units ;  some  of  these  will  be  ready  to 
unite  before  the  others,  and  we  may  have  systems 
containing  eight  units  formed  before  the  more  per- 
sistent of  those  containing  four,  three,  two  or  even 
one  unit  have  disappeared.  With  the  further  ad- 
vance of  aggregation  the  number  of  different  sys- 
tems present  at  one  and  the  same  time  will  in- 
crease. 

Thus,  if  we  regard  the  systems  containing  differ- 
ent numbers  of  units  as  corresponding  to  the 
different  chemical  elements,  then  as  the  universe 
gets  older  elements  of  higher  and  higher  atomic 
weight  may  be  expected  to  appear.  Their  appear- 
ance, however,  will  not  involve  the  annihilation  of 
the  elements  of  lower  atomic  weight.  The  number 
of  atoms  of  the  latter  will,  of  course,  diminish, 
since  the  heavier  elements  are  by  hypothesis  built 
up  of  material  furnished  by  the  lighter.  The  whole 


104  ELECTRICITY    AND   MATTER 

of  the  atoms  of  the  latter  would  not,  however,  all 
be  used  up  at  once,  and  thus  we  may  have  a  very 
large  number  of  elements  existing  at  one  and  the 
same  time. 

If,  however,  there  is  a  continual  fall  in  the  cor- 
puscular temperature  of  the  atoms  through  radia- 
tion, the  lighter  elements  will  disappear  in  time, 
and  unless  there  is  disintegration  of  the  heavier 
atoms,  the  atomic  weight  of  the  lightest  element 
surviving  will  continually  increase.  On  this  view, 
since  hydrogen  is  the  lightest  known  element  and 
the  atom  of  hydrogen  contains  about  a  thousand 
corpuscles,  all  aggregations  of  less  than  a  thousand 
units  have  entered  into  combination  and  are  no 
longer  free. 

The  way  the  Corpuscles  in  the  Atom  Lose  or  Gain 
Kinetic  Energy 

If  the  kinetic  energy  arising  from  the  motion  of 
the  corpuscles  relatively  to  the  centre  of  gravity 
of  the  atom  could  by  collisions  be  transformed 
into  kinetic  energy  due  to  the  motion  of  the  atom 
as  a  whole,  i.e.,  into  molecular  temperature,  it 
would  follow  from  the  kinetic  theory  of  gases, 
since  the  number  of  corpuscles  in  the  atom  is  ex- 
ceedingly large,  that  the  specific  heat  of  a  gas  at 


CONSTITUTION   OF   THE    ATOM  105 

constant  pressure  would  be  very  nearly  equal  to 
the  specific  heat  at  constant  volume  ;  whereas,  as 
a  matter  of  fact,  in  no  gas  is  there  any  approach 
to  equality  in  these  specific  heats.  We  conclude, 
therefore,  that  it  is  not  by  collisions  that  the 
kinetic  energy  of  the  corpuscles  is  diminished. 

We  have  seen,  however  (page  68),  that  a  mov- 
ing electrified  particle  radiates  energy  whenever 
its  velocity  is  changing  either  in  magnitude  or 
direction.  The  corpuscles  in  the  atom  will  thus 
emit  electric  waves,  radiating  energy  and  so  losing 
kinetic  energy. 

The  rate  at  which  energy  is  lost  in  this  way  by 
the  corpuscles  varies  very  greatly  with  the  num- 
ber of  the  corpuscles  and  the  way  in  which  they 
are  moving.  Thus,  if  we  have  a  single  corpuscle 
describing  a  circular  orbit  of  radius  a  with  uni- 
form velocity  v,  the  loss  of  energy  due  to  radia- 


o 
tion  per  second  is  -  ==-g,  where  e  is  the  charge  on 

O    V  Gb 

the  corpuscles  and  V  the  velocity  of  light.  If 
instead  of  a  single  corpuscle  we  had  two  corpus- 
cles at  opposite  ends  of  a  diameter  moving  round 
the  same  orbit  with  the  same  velocity  as  the  sin- 
gle corpuscle,  the  loss  of  energy  per  second  from  the 
two  would  be  very  much  less  than  from  the  single 


106  ELECTRICITY    AND    MATTER 

corpuscle,  and  the  smaller  the  velocity  of  the  cor- 
puscle the  greater  would  be  the  diminution  in 
the  loss  of  energy  produced  by  increasing  the 
number  of  corpuscles.  The  effect  produced  by 
increasing  the  number  of  corpuscles  is  shown  in 
the  following  table,  which  gives  the  rate  of  radia- 
tion for  each  corpuscle  for  various  numbers  of 
corpuscles  arranged  at  equal  angular  intervals 
round  the  circular  orbit. 

The  table  applies  to  two  cases  ;  in  one  the  veloc- 
ity of  the  corpuscles  is  taken  as  one-tenth  that  of 
light,  and  in  the  second  as  one-hundredth.  The 
radiation  from  a  single  corpuscle  is  in  each  case 
taken  as  unity. 

Number  of  corpuscles.        Radiation  from  each  corpuscle. 

_r  v^_ 

~~    10  "100 

1 1  1 

2 9.6xlO-2  9.6  x  10-4 

3 46  x  1C-3  4.6  x  10-7 

4 1.7  x  10-4  1.7  x  ICT10 

5 5.6  x  10-5  5.6  x  10-13 

6 1.6  x  10~7  1.6  x  10-n 

Thus,  we  see  that  the  radiation  from  each  of  a 
group  of  six  corpuscles  moving  with  one-tenth  the 
velocity  of  light  is  less  than  one-five-millionth  part 
of  the  radiation  from  a  single  corpuscle,  describ- 


CONSTITUTION    OF    THE    ATOM  1Q7 

ing  the  same  orbit  with  the  same  velocity,  while, 
when  the  velocity  of  the  corpuscles  is  only  one- 
hundredth  of  that  of  light,  the  reduction  in  the 
radiation  is  very  much  greater. 

If  the  corpuscles  are  displaced  from  the  sym- 
metrical position  in  which  they  are  situated  at 
equal  intervals  round  a  circle  whose  centre  is  at 
rest,  the  rate  of  radiation  will  be  very  much  in- 
creased. In  the  case  of  an  atom  containing  a  large 
number  of  corpuscles  the  variation  in  the  rate  at 
which  energy  is  radiated  will  vary  very  rapidly 
with  the  way  the  corpuscles  are  moving  about  in 
the  atom.  Thus,  for  example,  if  we  had  a  large 
number  of  corpuscles  following  close  on  one  an- 
other's heels  round  a  circular  orbit  the  radiation 
would  be  exceedingly  small ;  it  would  vanish  alto- 
gether if  the  corpuscles  were  so  close  together 
that  they  formed  a  continuous  ring  of  negative 
electrification.  If  the  same  number  of  particles 
were  moving  about  irregularly  in  the  atom,  then 
though  the  kinetic  energy  possessed  by  the  cor- 
puscles in  the  second  case  might  be  no  greater 
than  in  the  first,  the  rate  of  radiation,  i.e.,  of  cor- 
puscular cooling,  would  be  immensely  greater. 

Thus,  we  see  that  in  the  radiation  of  energy 
from  corpuscles  whose  velocity  is  not  uniform  we 


108  ELECTRICITY   AND   MATTER 

have  a  process  going  on  which  will  gradually  cool 
the  corpuscular  temperature  of  the  atom,  and  so, 
if  the  view  we  have  been  discussing  is  correct, 
enable  the  atom  to  form  further  aggregations  and 
thus  tend  to  the  formation  of  new  chemical  ele- 
ments. 

This  cooling  process  must  be  an  exceedingly 
slow  one,  for  although  the  corpuscular  tempera- 
ture when  the  atom  of  a  new  element  is  formed 
is  likely  to  be  exceedingly  high,  and  the  lowering 
in  that  temperature  required  before  the  atom  can 
enter  again  into  fresh  aggregations  very  large, 
yet  we  have  evidence  that  some  of  the  elements 
must  have  existed  unchanged  for  many  thousands, 
nay,  millions  of  years ;  we  have,  indeed,  no  direct 
evidence  of  any  change  at  all  in  the  atom.  I 
think,  however,  that  some  of  the  phenomena  of 
radio-activity  to  which  I  shall  have  to  allude  later, 
afford,  I  will  not  say  a  proof  of,  but  a  very  strong 
presumption  in  favor  of  some  such  secular  changes 
taking  place  in  the  atom. 

We  must  remember,  too,  that  the  corpuscles  in 
any  atom  are  receiving  and  absorbing  radiation 
from  other  atoms.  This  will  tend  to  raise  the 
corpuscular  temperature  of  the  atom  and  thus 
help  to  lengthen  the  time  required  for  that 


CONSTITUTION    OF   THE    ATOM  109 

temperature   to    fall  to    the    point  where  fresh 
aggregations  of  the  atom  may  be  formed. 

The  fact  that  the  rate  of  radiation  depends  so 
much  upon  the  way  the  corpuscles  are  moving 
about  in  the  atom  indicates  that  the  lives  of  the 
different  atoms  of  any  particular  element  will  not 
be  equal;  some  of  these  atoms  will  be  ready  to 
enter  upon  fresh  changes  long  before  the  others. 
It  is  important  to  realize  how  large  are  the 
amounts  of  energy  involved  in  the  formation  of  a 
complex  atom  or  in  any  rearrangement  of  the  con- 
figuration of  the  corpuscles  inside  it.  If  we  have 
an  atom  containing  n  corpuscles  each  with  a 
charge  e  measured  in  electrostatic  units,  the  total 
quantity  of  negative  electricity  in  the  atom  is  n  e 
and  there  is  an  equal  quantity  of  positive  elec- 
tricity distributed  through  the  sphere  of  positive 
electrification;  hence,  the  work  required  to  sep- 
arate the  atom  into  its  constituent  units  will  be 

comparable  with  ^ — ^ ,  a  being  the  radius  of  the 
a 

sphere  containing  the  corpuscles.      Thus,  as  the 
atom  has  been  formed  by  the  aggregation  of  these 

units  ^ne'   will  be  of  the  same  order  of  magni- 
a 

tude  as  the  kinetic  energy  imparted  to  those  con- 


ELECTRICITY   AND   MATTER 

stituents  during  their  whole  history,  from  the 
time  they  started  as  separate  units,  down  to  'the 
time  they  became  members  of  the  atom  under 
consideration.  They  will  in  this  period  have  radi- 
ated away  a  large  quantity  of  this  energy,  but  the 
following  calculation  will  show  what  an  enormous 
amount  of  kinetic  energy  the  corpuscles  in  the 
atom  must  possess  even  if  they  have  only  retained 
an  exceedingly  small  fraction  of  that  communi- 
cated to  them.  Let  us  calculate  the  value  of  {ne* 

a 

for  all  the  atoms  in  a  gram  of  the  substance ;  let 
JV  be  the  number  of  these  atoms  in  a  gram,  then 

N^ne^  is  the  value  of  the  energy  acquired  by  these 

d 

atoms.  If  M  is  the  mass  of  an  atom  JVM=  1,  thus : 


a         M    •  a 
but  if  m  is  the  mass  of  a  corpuscle 

nm  =1  M) 
and  therefore 

*T (n e)*        e   ne 


a  ma 

now  when  e  is  measured  in  electrostatic  units 

^_  =  3  X  1017  and  0  =  3.4  X  10"10 ; 
m 


CONSTITUTION    OF   THE    ATOM 

and  therefore 


N       *=  10.2  x  10  7  X  —  . 
a  a 

Let  us  take  the  case  of  the  hydrogen  atom  for 
which  n  =  1000,  and  take  for  a  the  value  usually 
assumed  in  the  kinetic  theory  of  gases  for  the 
radius  of  the  atom,  i.e.,  10"8  cm.  then 


=  ^02  x  1019ergs; 

this  amount  of  energy  would  be  sufficient  to  lift  a 
million  tons  through  a  height  considerably  ex- 
ceeding one  hundred  yards.  We  see,  too,  from 
(1)  that  this  energy  is  proportional  to  the  num- 
ber of  corpuscles,  so  that  the  greater  the  molecu- 
lar weight  of  an  element,  the  greater  will  be  the 
amount  of  energy  stored  up  in  the  atoms  in  each 
gram. 

We  shall  return  to  the  subject  of  the  internal 
changes  in  the  atom  when  we  discuss  some  of 
the  phenomena  of  radio-activity,  but  before  doing 
so  it  is  desirable  to  consider  more  closely  the  way 
the  corpuscles  arrange  themselves  in  the  atom. 
We  shall  begin  with  the  case  where  the  corpuscles 
are  at  rest.  The  corpuscles  are  supposed  to  be  in 
a  sphere  of  uniform  positive  electrification  which 
produces  a  radial  attractive  force  on  each  cor- 


112 


ELECTRICITY    AND    MATTER 


FIG.  16. 


puscle  proportional  to  its  distance  from  the  centre 
of  the  sphere,  and  the  problem  is  to  arrange  the 
corpuscles  in  the  sphere  so  that 
they  are  in  equilibrium  under  this 
attraction  and  their  mutual  re- 
pulsions. If  there  are  only  two 
corpuscles,  A  JBy  we  can  see  at 
once  that  they  will  be  in  equi- 
librium if  placed  so  that  A  B 
and  the  centre  of  the  sphere  are  in  the  same 
straight  line  and  OA  =  OB  =  \  the  radius  of  the 
sphere. 

If  there  are  three  corpuscles,  A  B  C,  they  will 
be  in  equilibrium  of  A  B  C  as  an  equilateral  tri- 
angle with  its  centre  at  O  and 
OA=OB=OC  =  ($l,  or  .57 
times  the  radius  of  the  sphere. 

If  there  are  four  corpuscles 
these  will  be  in  equilibrium  if 
placed  at  the  angular  points  of  a 
regular  tetrahedron  with  its  cen- 
tre at  the  centre  of  the  sphere.  In  these  cases  the 
corpuscles  are  all  on  the  surface  of  a  sphere  con- 
centric with  the  sphere  of  positive  electrification, 
and  we  might  suppose  that  whatever  the  number 
of  corpuscles  the  position  of  equilibrium  would  be 


FIG.  15. 


CONSTITUTION    OF   THE    ATOM 

one  of  symmetrical  distribution  over  the  surface 
of  a  sphere.  Such  a  distribution  would  indeed 
technically  be  one  of  equilibrium,  but  a  mathe- 
matical calculation  shows  that  unless  the  number 
of  corpuscles  is  quite  small,  say  seven  or  eight  at 
the  most,  this  arrangement  is  unstable  and  so  can 
never  persist.  When  the  number  of  corpuscles  is 
greater  than  this  limiting  number,  the  corpuscles 
break  up  into  two  groups.  One  group  containing 
the  smaller  number  of  corpuscles  is  on  the  surface 
of  a  small  body  concentric  with  the  sphere ;  the 
remainder  are  on  the  surface  of  a  larger  concen- 
tric body.  When  the  number  of  corpuscles  is 
still  further  increased  there  comes  a  stage  when 
the  equilibrium  cannot  be  stable  even  with  two 
groups,  and  the  corpuscles  now  divide  themselves 
into  three  groups,  arranged  on  the  surfaces  of  con- 
centric shells ;  and  as  we  go  on  increasing  the 
number  we  pass  through  stages  in  which  more  and 
more  groups  are  necessary  for  equilibrium.  With 
any  considerable  number  of  corpuscles  the  prob- 
lem of  finding  the  distribution  when  in  equilibrium 
becomes  too  complex  for  calculation ;  and  we  have 
to  turn  to  experiment  and  see  if  we  can  make  a 
model  in  which  the  forces  producing  equilibrium 
are  similar  to  those  we  have  supposed  to  be  at 


ELECTRICITY    AND    MATTER 

work  in  the  corpuscle.  Such  a  model  is  afforded 
by  a  very  simple  and  beautiful  experiment  first 
made,  I  think,  by  Professor  Mayer.  In  this  experi- 
ment a  number  of  little  magnets  are  floated  in  a 
vessel  of  water.  The  magnets  are  steel  needles 
magnetized  to  equal  strengths  and  are  floated  by 
being  thrust  through  small  disks  of  cork.  The 
magnets  are  placed  so  that  the  positive  poles  are 
either  all  above  or  all  below  the  surface  of  the 
water.  These  positive  poles,  like  the  corpuscles, 
repel  each  other  with  forces  varying  inversely  as 
the  distance  between  them.  The  attractive  force 
is  provided  by  a  negative  pole  (if  the  little  mag- 
nets have  their  positive  poles  above  the  water)  sus- 
pended some  distance  above  the  surface  of  the 
water.  This  pole  will  exert  on  the  positive  poles 
of  the  little  floating  magnets  an  attractive  force 
the  component  of  which,  parallel  to  the  surface 
of  the  water,  will  be  radial,  directed  to  O,  the 
projection  of  the  negative  pole  on  the  surface  of 
the  water,  and  if  the  negative  pole  is  some  dis- 
tance above  the  surface  the  component  of  the  force 
to  O  will  be  very  approximately  proportional  to 
the  distance  from  0.  Thus  the  forces  on  the  poles 
of  the  floating  magnets  will  be  very  similar  to  those 
acting  on  the  corpuscle  in  our  hypothetical  atom ; 


CONSTITUTION   OF   THE    ATOM 


115 


the  chief  difference  being  that  the  corpuscles  are 
free  to  move  about  in  all  directions  in  space,  while 
the  poles  of  the  floating  magnets  are  constrained 
to  move  in  a  plane  parallel  to  the  surface  of  the 
water. 

The  configurations  which  the  floating  magnets 
assume  as  the  number  of  magnets  increases  from 
two  up  to  nineteen  is  shown  in  Fig.  17,  which 
was  given  by  Mayer. 


FIG.  17. 


The  configuration  taken  up  when  the  magnets 
are  more  numerous  can  be  found  from  the  follow- 
ing table,  which  is  also  due  to  Mayer.  From  this 
table  it  will  be  seen  that  when  the  number  of 
floating  magnets  does  not  exceed  five  the  magnets 


116 


ELECTRICITY   AND   MATTER 


arrange  themselves  at  the  corners  of  a  regular 
polygon,  five  at  the  corners  of  a  pentagon,  four  at 
the  corners  of  a  square  and  so  on.  When  the 
number  is  greater  than  five  this  arrangement  no 
longer  holds.  Thus,  six  magnets  do  not  arrange 
themselves  at  the  corners  of  a  hexagon,  but  divide 
into  two  systems,  one  magnet  being  at  the  centre 
and  five  outside  it  at  the  corners  of  a  regular  penta- 
gon. This  arrangement  in  two  groups  lasts  until 
there  are  fifteen  magnets,  when  we  have  three 
groups ;  with  twenty-seven  magnets  we  get  four 
groups  and  so  on. 


Arrangement  of  Magnets  (Mayer) 


i. 


3. 


4, 


1  . 
1  . 
1  . 

5 

6 

7 

I2'6   i 

(2.7      ( 

3  . 
3  . 

7 
8 

I4''8 

(4.9 

I- 

9 

1  .  5 

1  .  6 

.  9 

.  9  - 

i2  .  7  .  10 
2  .  8  .  10 

3 
8 

.  7 
.  7 

10 
.  11 

4  .  8  .  12 
4  .  8  .  13 

J5  .  9 
\5  .  9 

.  12 
.  13 

1  .  6 
1  .  6 

.  10 
.  11 

2  .  7  .  11 

8 

3 

.  8 
.  8 

. 

.  11 

4  .  9  .  12 
^4  .  9  .  13 

3 

.  8 

.  12 

.3 

.  8 

.  13 

CONSTITUTION   OF   THE   ATOM 


1. 

5  .  9 

5  .  9 

6  .  9 


12  (  2  .  7  .  10  .  15 


13 
12 

6  .  10  .  12 
6  .  10  .  13 
6  .  11  .  12 
13 
14 


2  .  7  .  12 


6  .  11 
1  .  6  .  11 


.1  .  6  .   11  .  15 

Where,  for  example,  3.  7.  12.  13  means  that 
thirty-five  magnets  arrange  themselves  so  that 
there  is  a  ring  of  three  magnets  inside,  then  a  ring 
of  seven,  then  one  of  twelve,  and  one  of  thirteen 
outside. 

I  think  this  table  affords  many  suggestions  tow- 
ard the  explanation  of  some  of  the  properties 
possessed  by  atoms.  Let  us  take,  for  example,  the 
chemical  law  called  the  Periodic  Law  ;  according 
to  this  law  if  we  arrange  the  elements  in  order  of 
increasing  atomic  weights,  then  taking  an  element 
of  low  atomic  weight,  say  lithium,  we  find  certain 
properties  associated  with  it.  These  properties 
are  not  possessed  by  the  elements  immediately 
following  it  in  the  series  of  increasing  atomic 
weight  ;  but  they  appear  again  when  we  come  to 
sodium,  then  they  disappear  again  for  a  time, 


;Qg  ELECTRICITY   AND   MATTER 

but  reappear  when  we  reach  potassium,  and  so 
on.  Let  us  now  consider  the  arrangements  of 
the  floating  magnets,  and  suppose  that  the  number 
of  magnets  is  proportional  to  the  combining  weight 
of  an  element.  Then,  if  any  property  were  asso- 
ciated with  the  triangular  arrangement  of  magnets, 
it  would  be  possessed  by  the  elements  whose  com- 
bining weight  was  on  this  scale  three,  but  would 
not  appear  again  until  we  reached  the  combining 
weight  ten,  when  it  reappears,  as  for  ten  magnets 
we  have  the  triangular  arrangement  in  the  middle 
and  a  ring  of  seven  magnets  outside.  When  the 
number  of  magnets  is  increased  the  triangular 
arrangement  disappears  for  a  time,  but  reappears 
with  twenty  magnets,  and  again  with  thirty-five, 
the  triangular  arrangement  appearing  and  dis- 
appearing in  a  way  analogous  to  the  behavior  of 
the  properties  of  the  elements  in  the  Periodic 
Law.  As  an  example  of  a  property  that  might 
very  well  be  associated  with  a  particular  grouping 
of  the  corpuscles,  let  us  take  the  times  of  vibra- 
tion of  the  system,  as  shown  by  the  position  of 
the  lines  in  the  spectrum  of  the  element.  First 
let  us  take  the  case  of  three  corpuscles  by  them- 
selves in  the  positively  electrified  sphere.  The 
three  corpuscles  have  nine  degrees  of  freedom,  so 


CONSTITUTION   OF   THE    ATOM 

that  there  are  nine  possible  periods.  Some  of 
these  periods  in  this  case  would  be  infinitely  long, 
and  several  of  the  possible  periods  would  be  equal 
to  each  other,  so  that  we  should  not  get  nine  dif- 
ferent periods. 

Suppose  that  the  lines  in  the  spectrum  of  the 
three  corpuscles  are  as  represented  in  Fig.  18  #, 

A        B     C     D     £ 


^  3    /    2 


c    o    t 


A      B 


FIG.  18. 


0     £ 


where  the  figures  under  the  lines  represent  the 
number  of  periods  which  coalesce  at  that  line ;  i.e., 
regarding  the  periods  as  given  by  an  equation  with 
nine  roots,  we  suppose  that  there  is  only  one  root 
giving  the  period  corresponding  to  the  line  A, 
while  corresponding  to  B  there  are  two  equal 
roots,  three  equal  roots  corresponding  to  C,  one 


120  ELECTRICITY    AND   MATTER 

root,  to  O,  and  two  to  E.  These  periods  would 
have  certain  numerical  relations  to  each  other,  in- 
dependent of  the  charge  on  the  corpuscle,  the  size 
of  the  sphere  in  which  they  are  placed,  or  their 
distance  from  the  centre  of  the  sphere.  Each  of 
these  quantities,  although  it  does  not  affect  the 
ratio  of  the  periods,  will  have  a  great  effect  upon 
the  absolute  value  of  any  one  of  them.  Now, 
suppose  that  these  three  corpuscles,  instead  of 
being  alone  in  the  sphere,  form  but  one  out  of 
several  groups  in  it,  just  as  the  triangle  of  mag- 
nets forms  a  constituent  of  the  grouping  of  3,  10, 
20,  and  35  magnets.  Let  us  consider  how  the 
presence  of  the  other  groups  would  affect  the 
periods  of  vibration  of  the  three  corpuscles.  The 
absolute  values  of  the  periods  would  generally  be 
entirely  different,  but  the  relationship  existing  be- 
tween the  various  periods  would  be  much  more 
persistent,  and  although  it  might  be  modified  it 
would  not  be  destroyed.  Using  the  phraseology  of 
the  Planetary  Theory,  we  may  regard  the  motion 
of  the  three  corpuscles  as  "  disturbed  "  by  the 
other  groups. 

When  the  group  of  three  corpuscles  was  by  it- 
self there  were  several  displacements  which  gave 
the  same  period  of  vibration ;  for  example,  corre- 


CONSTITUTION    OF    THE    ATOM  121 

spending  to  the  line  O  there  were  three  displace- 
ments, all  giving  the  same  period.  When,  how* 
ever,  there  are  other  groups  present,  then  these 
different  displacements  will  no  longer  be  sym- 
metrical with  respect  to  these  groups,  so  that  the 
three  periods  will  no  longer  be  quite  equal.  They 
would,  however,  be  very  nearly  equal  unless  the 
effect  of  the  other  groups  is  very  large.  Thus, 
in  the  spectrum,  (7,  instead  of  being  a  single  line, 
would  become  a  triplet,  while  B  and  E  would  be- 
come doublets.  A  D  would  remain  single  lines. 

Thus,  the  spectrum  would  now  resemble  Fig. 
185;  the  more  groups  there  are  surrounding  the 
group  of  three  the  more  will  the  motion  of  the 
latter  be  disturbed  and  the  greater  the  separation 
of  the  constituents  of  the  triplets  and  doublets. 
The  appearance  as  the  number  of  groups  increases 
is  shown  in  Fig.  18  #,  c.  Thus,  if  we  regarded 
the  element  which  contain  this  particular  group- 
ing of  corpuscles  as  being  in  the  same  group  in  the 
classification  of  elements  according  to  the  Periodic 
Law,  we  should  get  in  the  spectra  of  these  ele- 
ments homologous  series  of  lines,  the  distances  be- 
tween the  components  of  the  doublets  and  triplets 
increasing  with  the  atomic  weight  of  the  elements. 
The  investigations  of  Kydberg,  Kunge  and  Pas- 


122  ELECTRICITY   AND   MATTER 

chen  and  Keyser  have  shown  the  existence  in  the 
spectra  of  elements  of  the  same  group  series  of 
lines  having  properties  in  many  respects  analogous 
to  those  we  have  described. 

Another  point  of  interest  given  by  Mayer's  ex- 
periments is  that  there  is  more  than  one  stable 
configuration  for  the  same  number  of  magnets; 
these  configurations  correspond  to  different  amounts 
of  potential  energy,  so  that  the  passage  from  the 
configuration  of  greater  potential  energy  to  that  of 
less  would  give  kinetic  energy  to  the  corpuscle. 
From  the  values  of  the  potential  energy  stored 
in  the  atom,  of  which  we  gave  an  estimate  on 
page  111,  we  infer  that  a  change  by  even  a  small 
fraction  in  that  potential  energy  would  develop 
an  amount  of  kinetic  energy  which  if  converted 
into  heat  would  greatly  transcend  the  amount  of 
heat  developed  when  the  atoms  undergo  any  known 
chemical  combination. 

An  inspection  of  the  table  shows  that  there  are 
certain  places  in  it  where  the  nature  of  the  con- 
figuration changes  very  rapidly  with  the  number 
of  magnets ;  thus,  five  magnets  form  one  group, 
while  six  magnets  form  two ;  fourteen  magnets 
form  two  groups,  fifteen  three ;  twenty  -  seven 
magnets  form  three  groups,  twenty-eight  four, 


CONSTITUTION    OF    THE    ATOM  123 

and  so  on.  If  we  arrange  the  chemical  elements 
in  the  order  of  their  atomic  weights  we  find  there 
are  certain  places  where  the  difference  in  proper- 
ties of  consecutive  elements  is  exceptionally  great ; 
thus,  for  example,  we  have  extreme  differences  in 
properties  between  fluorine  and  sodium.  Then 
there  is  more  or  less  continuity  in  the  properties 
until  we  get  to  chlorine,  which  is  followed  by 
potassium;  the  next  break  occurs  at  bromine 
and  rubidium  and  so  on.  This  effect  seems 
analogous  to  that  due  to  the  regrouping  of  the 
magnets. 

So  far  we  have  supposed  the  corpuscles  to  be 
at  rest ;  if,  however,  they  are  in  a  state  of  steady 
motion  and  describing  circular  orbits  round  the 
centre  of  the  sphere,  the  effect  of  the  centrifugal 
force  arising  from  this  motion  will  be  to  drive  the 
corpuscles  farther  away  from  the  centre  of  the 
sphere,  without,  in  many  cases,  destroying  the 
character  of  the  configuration.  Thus,  for  example, 
if  we  have  three  corpuscles  in  the  sphere,  they 
will,  in  the  state  of  steady  motion,  as  when  they 
are  at  rest,  be  situated  at  the  corners  of  an  equi- 
angular triangle ;  this  triangle  will,  however,  be 
rotating  round  the  centre  of  the  sphere,  and  the 
distance  of  the  corpuscles  from  the  centre  will  be 


124  ELECTRICITY    AND    MATTER 

greater  than  when  they  are  at  rest  and  will  in- 
crease with  the  velocity  of  the  corpuscles. 

There  are,  however,  many  cases  in  which  rota- 
tion is  essential  for  the  stability  of  the  configura- 
tion. Thus,  take  the  case  of  four  corpuscles. 
These,  if  rotating  rapidly,  are  in  stable  steady 
motion  when  at  the  corners  of  a  square,  the  plane 
of  the  square  being  at  right  angles  to  the  axis  of 
rotation ;  when,  however,  the  velocity  of  rotation 
of  the  corpuscles  falls  below  a  certain  value,  the 
arrangement  of  four  corpuscles  in  one  plane  be- 
comes unstable,  and  the  corpuscles  tend  to  place 
themselves  at  the  corners  of  a  regular  tetrahedron, 
which  is  the  stable  arrangement  when  the  cor- 
puscles are  at  rest.  The  system  of  four  corpuscles 
at  the  corners  of  a  square  may  be  compared  with 
a  spinning  top,  the  top  like  the  corpuscles  being 
unstable  unless  its  velocity  of  rotation  exceeds 
a  certain  critical  value.  Let  us  suppose  that 
initially  the  velocity  of  the  corpuscles  exceeds 
this  value,  but  that  in  some  way  or  another  the 
corpuscles  gradually  lose  their  kinetic  energy; 
the  square  arrangement  will  persist  until  the  ve- 
locity of  the  corpuscles  is  reduced  to  the  critical 
value.  The  arrangement  will  then  become  un- 
stable, and  there  will  be  a  convulsion  in  the  sys- 


CONSTITUTION    OF   THE   ATOM  125 

tern  accompanied  by  a  great  evolution  of  kinetic 
energy. 

Similar  considerations  will  apply  to  many  as- 
semblages of  corpuscles.  In  such  cases  the  con- 
figuration when  the  corpuscles  are  rotating  with 
great  rapidity  will  (as  in  the  case  of  the  four  cor- 
puscles) be  essentially  different  from  the  configu- 
ration of  the  same  number  of  corpuscles  when  at 
rest.  Hence  there  must  be  some  critical  velocity 
of  the  corpuscles,  such  that,  for  velocities  greater 
than  the  critical  one,  a  configuration  is  stable, 
which  becomes  unstable  when  the  velocity  is 
reduced  below  the  critical  value.  When  the  ve- 
locity sinks  below  the  critical  value,  instability 
sets  in,  and  there  is  a  kind  of  convulsion  or  ex- 
plosion, accompanied  by  a  great  diminution  in  the 
potential  energy  and  a  corresponding  increase  in 
the  kinetic  energy  of  the  corpuscles.  This  increase 
in  the  kinetic  energy  of  the  corpuscles  may  be 
sufficient  to  detach  considerable  numbers  of  them 
from  the  original  assemblage. 

These  considerations  have  a  very  direct  bearing 
on  the  view  of  the  constitution  of  the  atoms  which 
we  have  taken  in  this  chapter,  for  they  show  that 
with  atoms  of  a  special  kind,  i.e.,  with  special 
atomic  weights,  the  corpuscular  cooling  caused  by 


126  ELECTRICITY    AND   MATTER 

the  radiation  from  the  moving  corpuscles  which 
we  have  supposed  to  be  slowly  going  on,  might, 
when  it  reached  a  certain  stage,  produce  instabil- 
ity inside  the  atom,  and  produce  such  an  in- 
crease in  the  kinetic  energy  of  the  corpuscles  as 
to  give  rise  to  greatly  increased  radiation,  and  it 
might  be  detachment  of  a  portion  of  the  atom. 
It  would  cause  the  atom  to  emit  energy ;  this 
energy  being  derived  from  the  potential  energy 
due  to  the  arrangement  of  the  corpuscles  in  the 
atom.  We  shall  see  when  we  consider  the  phe- 
nomenon of  radio-activity  that  there  is  a  class  of 
bodies  which  show  phenomena  analogous  to  those 
just  described. 

On  the  view  that  the  lighter  elements  are 
formed  first  by  the  aggregation  of  the  unit 
doublet,  the  negative  element  of  which  is  the  cor- 
puscle, and  that  it  is  by  the  combination  of  the 
atoms  of  the  lighter  elements  that  the  atoms  of 
the  heavier  elements  are  produced,  we  should  ex- 
pect the  corpuscles  in  the  heavy  atoms  to  be  ar- 
ranged as  it  were  in  bundles,  the  arrangement  of 
the  corpuscles  in  each  bundle  being  similar  to  the 
arrangement  in  the  atom  of  some  lighter  element. 
In  the  heavier  atom  these  bundles  would  act  as 
subsidiary  units,  each  bundle  corresponding  to 


CONSTITUTION    OF   THE    ATOM  127 

one  of  the  magnets  in  the  model  formed  by  the 
floating  magnets,  while  inside  the  bundle  them- 
selves the  corpuscle  would  be  the  analogue  of 
the  magnet. 

We  must  now  go  on  to  see  whether  an  atom 
built  up  in  the  way  we  have  supposed  could  pos- 
sess any  of  the  properties  of  the  real  atom.  Is 
there,  for  example,  in  this  model  of  an  atom  any 
scope  for  the  electro-chemical  properties  of  the 
real  atom ;  such  properties,  for  example,  as  those 
illustrated  by  the  division  of  the  chemical  ele- 
ments into  two  classes,  electro-positive  and  electro- 
negative. Why,  for  example,  if  this  is  the  con- 
stitution of  the  atom,  does  an  atom  of  sodium  or 
potassium  tend  to  acquire  a  positive,  the  atom  of 
chlorine  a  negative  charge  of  electricity  ?  Again, 
is  there  anything  in  the  model  of  the  atom  to 
suggest  the  possession  of  such  a  property  as  that 
called  by  the  chemists  valency  ;  i.e.,  the  property 
which  .  enables  us  to  divide  the  elements  into 
groups,  called  monads,  dyads,  triads,  such  that  in 
a  compound  formed  by  any  two  elements  of  the 
first  group  the  molecule  of  the  compound  will 
contain  the  same  number  of  atoms  of  each  element, 
while  in  a  compound  formed  by  an  element  A  in 
the  first  group  with  one  B  in  the  second,  the  mole- 


ELECTRICITY   AND   MATTER 

cule  of  the   compound   contains   twice  as  many 
atoms  of  A  as  of  B,  and  so  on  \ 

Let  us  now  turn  to  the  properties  of  the  model 
atom.  It  contains  a  very  large  number  of  corpus- 
cles in  rapid  motion.  We  have  evidence  from  the 
phenomena  connected  with  the  conduction  of 
electricity  through  gases  that  one  or  more  of  these 
corpuscles  can  be  detached  from  the  atom. 
These  may  escape  owing  to  their  high  veloc- 
ity enabling  them  to  travel  beyond  the  attrac- 
tion of  the  atom.  They  may  be  detached  also  by 
collision  of  the  atom  with  other  rapidly  moving 
atoms  or  free  corpuscles.  When  once  a  corpuscle 
has  escaped  from  an  atom  the  latter  will  have  a  pos- 
itive charge.  This  will  make  it  more  difficult  for 
a  second  negatively  electrified  corpuscle  to  escape, 
for  in  consequence  of  the  positive  charge  on  the 
atom  the  latter  will  attract  the  second  corpuscle 
more  strongly  than  it  did  the  first.  Now  we  can 
readily  conceive  that  the  ease  with  which  a  par- 
ticle will  escape  from,  or  be  knocked  out  of,  an 
atom  may  vary  very  much  in  the  atoms  of  the  dif- 
ferent elements.  In  some  atoms  the  velocities  of 
the  corpuscles  may  be  so  great  that  a  corpuscle 
escapes  at  once  from  the  atom.  It  may  even  be 
that  after  one  has  escaped,  the  attraction  of  the 


CONSTITUTION    OF   THE    ATOM  129 

positive  electrification  thus  left  on  the  atom  is 
not  sufficient  to  restrain  a  second,  or  even  a  third, 
corpuscle  from  escaping.  Such  atoms  would  ac- 
quire positive  charges  of  one,  two,  or  three  units, 
according  as  they  lost  one,  two,  or  three  corpus- 
cles. On  the  other  hand,  there  may  be  atoms  in 
which  the  velocities  of  the  corpuscles  are  so  small 
that  few,  if  any,  corpuscles  escape  of  their  own 
accord,  nay,  they  may  even  be  able  to  receive 
one  or  even  more  than  one  corpuscle  before  the 
repulsion  exerted  by  the  negative  electrification 
on  these  foreign  corpuscles  forces  any  of  the 
original  corpuscles  out.  Atoms  of  this  kind  if 
placed  in  a  region  where  corpuscles  were  present 
would  by  aggregation  with  these  corpuscles  re. 
ceive  a  negative  charge.  The  magnitude  of  the 
negative  charge  would  depend  upon  the  firmness 
with  which  the  atom  held  its  corpuscles.  If  a 
negative  charge  of  one  corpuscle  were  not  suf- 
ficient to  expel  a  corpuscle  while  the  negative 
charge  of  two  corpuscles  could  do  so,  the  maxi- 
mum negative  charge  on  the  atom  would  be  one 
unit.  If  two  corpuscles  were  not  sufficient  to  expel 
a  corpuscle,  but  three  were,  the  maximum  nega- 
tive charge  would  be  two  units,  and  so  on.  Thus, 
the  atoms  of  this  class  tend  to  get  charged  with 


130  ELECTRICITY    AND   MATTER 

negative  electricity  and  correspond  to  the  electro- 
negative chemical  elements,  while  the  atoms  of  the 
class  we  first  considered,  and  which  readily  lose 
corpuscles,  acquire  a  positive  charge  and  corre- 
spond to  the  atoms  of  the  electro-positive  elements. 
We  might  conceive  atoms  in  which  the  equilib- 
rium of  the  corpuscles  was  so  nicely  balanced 
that  though  they  do  not  of  themselves  lose  a  cor- 
puscle, and  so  do  not  acquire  a  positive  charge,  the 
repulsion  exerted  by  a  foreign  corpuscle  coming 
on  to  the  atom  would  be  sufficient  to  drive  out  a 
corpuscle.  Such  an  atom  would  be  incapable  of 
receiving  a  charge  either  of  positive  or  negative 
electricity. 

Suppose  we  have  a  number  of  the  atoms  that 
readily  lose  their  corpuscles  mixed  with  a  num- 
ber of  those  that  can  retain  a  foreign  corpuscle. 
Let  us  call  an  atom  of  the  first  class  A,  one  of  the 
second  B,  and  suppose  that  the  A  atoms  are  of 
the  kind  that  lose  one  corpuscle  while  the  B  atoms 
are  of  the  kind  that  can  retain  one,  but  not  more 
than  one  ;  then  the  corpuscles  which  escape  from 
the  A  atoms  will  ultimately  find  a  home  on  the  B 
atoms,  and  if  there  are  an  equal  number  of  the 
two  kinds  of  atoms  present  we  shall  get  ultimate- 
ly all  the  A  atoms  with  the  unit  positive  charge, 


CONSTITUTION   OF   THE   ATOM  131 

all  the  B  atoms  with  the  unit  negative  charge. 
These  oppositely  electrified  atoms  will  attract  each 
other,  and  we  shall  get  the  compound  A  B 
formed.  If  the  A  atoms  had  been  of  the  kind 
that  lost  two  corpuscles,  and  the  B  atoms  the 
same  as  before,  then  the  A  atoms  would  get  the 
charge  of  two  positive  units,  the  B  atoms  a  charge 
of  one  unit  of  negative  electricity.  Thus,  to  form 
a  neutral  system  two  of  the  B  atoms  must  com- 
bine with  one  of  the  A1^  and  thus  the  compound 
A  BI  would  be  formed. 

Thus,  from  this  point  of  view  a  univalent  elec- 
tro-positive atom  is  one  which,  under  the  circum- 
stances prevailing  when  combination  is  taking 
place,  has  to  lose  one  and  only  one  corpuscle  be- 
fore stability  is  attained ;  a  univalent  electro-neg- 
ative atom  is  one  which  can  receive  one  but  not 
more  than  one  corpuscle  without  driving  off  other 
corpuscles  from  the  atom;  a  divalent  electro- 
positive atom  is  one  that  loses  two  corpuscles  and 
no  more,  and  so  on.  The  valency  of  the  atom 
thus  depends  upon  the  ease  with  which  corpus- 
cles can  escape  from  or  be  received  by  the  atom  ; 
this  may  be  influenced  by  the  circumstances 
existing  when  combination  is  taking  place.  Thus, 
it  would  be  easier  for  a  corpuscle,  when  once  it 


132  ELECTRICITY   AND   MATTER 

had  got  outside  the  atom,  to  escape  being  pulled 
back  again  into  it  by  the  attraction  of  its  positive 
electrification,  if  the  atom  were  surrounded  by  good 
conductors  than  if  it  were  isolated  in  space.  We 
can  understand,  then,  why  the  valency  of  an  atom 
may  in  some  degree  be  influenced  by  the  physical 
conditions  under  which  combination  is  taking  place. 
On  the  view  that  the  attraction  between  the 
atoms  in  a  chemical  compound  is  electrical  in  its 
origin,  the  ability  of  an  element  to  enter  into 
chemical  combination  depends  upon  its  atom  hav- 
ing the  power  of  acquiring  a  charge  of  electricity. 
This,  on  the  preceding  view,  implies  either  that  the 
uncharged  atom  is  unstable  and  has  to  lose  one  or 
more  corpuscles  before  it  can  get  into  a  steady 
state,  or  else  that  it  is  so  stable  that  it  can  retain 
one  or  more  additional  corpuscles  without  any  of 
the  original  corpuscles  being  driven  out.  If  the 
range  of  stability  is  such  that  the  atom,  though 
stable  when  uncharged,  becomes  unstable  when  it 
receives  an  additional  corpuscle,  the  atom  will  not 
be  able  to  receive  a  charge  either  of  positive  or 
negative  electricity,  and  will  therefore  not  be  able 
to  enter  into  chemical  combination.  Such  an  atom 
would  have  the  properties  of  the  atoms  of  such 
elements  as  argon  or  helium. 


CONSTITUTION    OF    THE    ATOM  133 

The  view  that  the  forces  which  bind  together 
the  atoms  in  the  molecules  of  chemical  compounds 
are  electrical  in  their  origin,  was  first  proposed 
by  Berzelius ;  it  was  also  the  view  of  Davy  and  of 
Faraday.  Helmholtz,  too,  declared  that  the 
mightiest  of  the  chemical  forces  are  electrical  in 
their  origin.  Chemists  in  general  seem,  however, 
to  have  made  but  little  use  of  this  idea,  having 
apparently  found  the  conception  of  "  bonds  of 
affinity"  more  fruitful.  This  doctrine  of  bonds 
is,  however,  when  regarded  in  one  aspect  almost 
identical  with  the  electrical  theory.  The  theory 
of  bonds  when  represented  graphically  supposes 
that  from  each  univalent  atom  a  straight  line 
(the  symbol  of  a  bond)  proceeds;  a  divalent 
atom  is  at  the  end  of  two  such  lines,  a  trivalent 
atom  at  the  end  of  three,  and  so  on ;  and  that 
when  the  chemical  compound  is  represented  by  a 
graphic  formula  in  this  way,  each  atom  must  be 
at  the  end  of  the  proper  number  of  the  lines 
which  represent  the  bonds.  Now,  on  the  electrical 
view  of  chemical  combination,  a  univalent  atom 
has  one  unit  charge,  if  we  take  as  our  unit  of 
charge  the  charge  on  the  corpuscle ;  the  atom  is 
therefore  the  beginning  or  end  of  one  unit  Fara- 
day tube  :  the  beginning  if  the  charge  on  the 


134  ELECTRICITY   AND   MATTER 

atom  is  positive,  the  end  if  the  charge  is  nega- 
tive. A  divalent  atom  has  two  units  of  charge  and 
therefore  it  is  the  origin  or  termination  of  two 
unit  Faraday  tubes.  Thus,  if  we  interpret  the 
"bond"  of  the  chemist  as  indicating  a  unit  Fara- 
day tube,  connecting  charged  atoms  in  the  mole- 
cule, the  structural  formulae  of  the  chemist  can 
be  at  once  translated  into  the  electrical  theory. 
There  is,  however,  one  point  of  difference  which 
deserves  a  little  consideration :  the  symbol  indi- 
cating a  bond  on  the  chemical  theory  is  not  re- 
garded as  having  direction  ;  no  difference  is  made 
on  this  theory  between  one  end  of  a  bond  and 
the  other.  On  the  electrical  theory,  however,  there 
is  a  difference  between  the  ends,  as  one  end  cor- 
responds to  a  positive,  the  other  to  a  negative 
charge.  An  example  or  two  may  perhaps  be  the 
easiest  way  of  indicating  the  effect  of  this  consid- 
eration. Let  us  take  the  gas  ethane  whose  structu- 
ral formula  is  written 


According  to  the  chemical  view  there  is  no  differ- 


CONSTITUTION    OF   THE    ATOM 

ence  between  the  two  carbon  atoms  in  this  com- 
pound ;  there  would,  however,  be  a  difference  on 
the  electrical  view.  For  let  us  suppose  that  the 
hydrogen  atoms  are  all  negatively  electrified;  the 
three  Faraday  tubes  going  from  the  hydrogen  atoms 
to  each  carbon  atom  give  a  positive  charge  of 
three  units  on  each  carbon  atom.  But  in  addition 
to  the  Faraday  tubes  coming  from  the  hydrogen 
atoms,  there  is  one  tube  which  goes  from  one  car- 
bon atom  to  the  other.  This  means  an  additional 
positive  charge  on  one  carbon  atom  and  a  nega- 
tive charge  on  the  other.  Thus,  one  of  the  carbon 
atoms  will  have  a  charge  of  four  positive  units, 
while  the  other  will  have  a  charge  of  three  positive 
and  one  negative  unit,  £&,  two  positive  units ;  so 
that  on  this  view  the  two  carbon  atoms  are  not  in 
the  same  state.  A  still  greater  difference  must 
exist  between  the  atoms  when  we  have  what  is 
called  double  linking,  i.e.,  when  the  carbon  atoms 
are  supposed  to  be  connected  by  two  bonds,  as  in 
the  compound 


136  ELECTRICITY    AND    MATTER 

Here,  if  one  carbon  atom  had  a  charge  of  four  posi- 
tive units,  the  other  would  have  a  charge  of  two 
positive  and  two  negative  units. 

We  might  expect  to  discover  such  differences 
as  are  indicated  by  these  considerations  by  the  in- 
vestigation of  which  are  known  as  additive  prop- 
erties, i.e.,  properties  which  can  be  calculated 
when  the  chemical  constitution  of  the  molecule 
is  known.  Thus,  let  ABC  represent  the  atoms  of 
three  chemical  elements,  then  if  p  is  the  value  of 
some  physical  constant  for  the  molecule  of  A^ 
q  the  value  for  B^  and  r  for  C^  then  if  this  con- 
stant obeys  the  additive  law,  its  value  for  a  mole- 
cule of  the  substance  whose  chemical  composition 
is  represented  by  the  formula  A&  B7  Cz  is 


We  can  only  expect  relations  like  this  to  hold  when 
the  atoms  which  occur  in  the  different  compounds 
corresponding  to  different  values  of  x  y  z  are 
the  same.  If  the  atom  A  occurs  in  different  states 
in  different  compounds  we  should  have  to  use 
different  values  of  p  for  these  compounds. 

A  well-known  instance  of  the  additive  prop- 
erty is  the  refractive  power  of  different  substances 
for  light,  and  in  this  case  chemists  find  it  neces- 


CONSTITUTION    OF   THE    ATOM  137 

sary  to  use  different  values  for  the  refraction  due 
a  carbon  atom  according  as  the  atom  is  doubly  or 
singly  linked.  They  use,  however,  the  same  value 
for  the  refraction  of  the  carbon  atom  when  singly 
linked  with  another  atom  as  when,  as  in  the  com- 
pound C  H±,  it  is  not  linked  with  another  carbon 
atom  at  all. 

It  may  be  urged  that  although  we  can  conceive 
that  one  atom  in  a  compound  should  be  positively 
and  the  other  negatively  electrified  when  the 
atoms  are  of  different  kinds,  it  is  not  easy  to  do 
so  when  the  atoms  are  of  the  same  kind,  as  they 
are  in  the  molecules  of  the  elementary  gases 
HI,  O2j  -2V^  and  so  on.  With  reference  to  this 
point  we  may  remark  that  the  electrical  state  of 
an  atom,  depending  as  it  does  on  the  power  of 
the  atom  to  emit  or  retain  corpuscles,  may  be  very 
largely  influenced  by  circumstances  external  to 
the  atom.  Thus,  for  an  example,  an  atom  in  a  gas 
when  surrounded  by  rapidly  moving  atoms  or 
corpuscles  which  keep  striking  against  it  may 
have  corpuscles  driven  out  of  it  by  these  collisions 
and  thus  become  positively  electrified.  On  the 
other  hand,  we  should  expect  that,  ceteris  paribus, 
the  atom  would  be  less  likely  to  lose  a  corpuscle 
when  it  is  in  a  gas  than  when  in  a  solid  or  a 


138  ELECTRICITY    AND    MATTER 

liquid.  For  when  in  a  gas  after  a  corpuscle  has 
just  left  the  atom  it  has  nothing  beyond  its  own 
velocity  to  rely  upon  to  escape  from  the  attraction 
of  the  positively  electrified  atom,  since  the  other 
atoms  are  too  far  away  to  exert  any  forces  upon 
it.  When,  however,  the  atom  is  in  a  liquid  or  a 
solid,  the  attractions  of  the  other  atoms  which 
crowd  round  this  atom  may,  when  once  a  corpus- 
cle has  left  its  atom,  help  it  to  avoid  falling 
back  again  into  atom.  As  an  instance  of  this 
effect  we  may  take  the  case  of  mercury  in  the 
liquid  and  gaseous  states.  In  the  liquid  state 
mercury  is  a  good  conductor  of  electricity.  One 
way  of  regarding  this  electrical  conductivity  is 
to  suppose  that  corpuscles  leave  the  atoms  of  the 
mercury  and  wander  about  through  the  inter- 
stices between  the  atoms.  These  charged  cor- 
puscles when  acted  upon  by  an  electric  force 
are  set  in  motion  and  constitute  an  electric  cur- 
rent, the  conductivity  of  the  liquid  mercury  in- 
dicating the  presence  of  a  large  number  of  cor- 
puscles. When,  however,  mercury  is  in  the  gaseous 
state,  its  electrical  conductivity  has  been  shown  by 
Strutt  to  be  an  exceedingly  small  fraction  of  the 
conductivity  possessed  by  the  same  number  of 
molecules  when  gaseous.  We  have  thus  indications 


CONSTITUTION    OF   THE    ATOM  139 

that  the  atoms  even  of  an  electro-positive  sub- 
stance like  mercury  may  only  lose  comparatively 
few  corpuscles  when  in  the  gaseous  state.  Sup- 
pose then  that  we  had  a  great  number  of  atoms 
all  of  one  kind  in  the  gaseous  state  and  thus  mov- 
ing about  and  coming  into  collision  with  each 
other;  the  more  rapidly  moving  ones,  since  they 
would  make  the  most  violent  collisions,  would  be 
more  likely  to  lose  corpuscles  than  the  slower 
ones.  The  faster  ones  would  thus  by  the  loss  of 
their  corpuscles  become  positively  electrified, 
while  the  corpuscles  driven  off  would,  if  the 
atoms  were  not  too  electro-positive  to  be  able  to 
retain  a  negative  charge  even  when  in  the  gase- 
ous state,  tend  to  find  a  home  on  the  more  slowly 
moving  atoms.  Thus,  some  of  the  atoms  would 
get  positively,  others  negatively  electrified,  and 
those  with  changes  of  opposite  signs  would  com- 
bine to  form  a  diatomic  molecule.  This  argu- 
ment would  not  apply  to  very  electro-positive 
gases.  These  we  should  not  expect  to  form  mole- 
cules, but  since  there  would  be  many  free  cor- 
puscles in  the  gas  we  should  expect  them  to 
possess  considerable  electrical  conductivity. 


CHAPTER  VI 

RADIO-ACTIVITY  AND   KADIO-ACTIVE   SUB- 
STANCES 

IN  1896  Becquerel  discovered  that  uranium 
and  its  salts  possess  the  power  of  giving  out  rays 
which,  like  Rontgen  and  cathode  rays,  affect  a 
photographic  plate,  and  make  a  gas  through  which 
they  pass  a  conductor  of  electricity.  In  1898 
Schmidt  discovered  that  thorium  possesses  similar 
properties.  This  power  of  emitting  rays  is  called 
radio-activity,  and  substances  which  possess  the 
power  are  said  to  be  radio-active. 

This  property  of  uranium  led  to  a  careful  ex- 
amination of  a  large  number  of  minerals  contain- 
ing this  substance,  and  M.  and  Mme.  Curie  found 
that  some  of  these,  and  notably  some  specimens  of 
pitch-blende,  were  more  radio-active  than  equal 
volumes  of  pure  uranium,  although  only  a  fraction 
of  these  minerals  consisted  of  uranium.  This  in- 
dicated that  these  minerals  contained  a  substance 
or  substances  much  more  radio-active  than  uran- 
ium itself,  and  a  systematic  attempt  was  made  to 


RADIO-ACTIVE    SUBSTANCES  141 

isolate  these  substances.  After  a  long  investigation, 
conducted  with  marvellous  skill  and  perseverance, 
M.  and  Mme.  Curie,  with  the  collaboration  of  MM. 
Bemont  and  Debierne,  succeeded  in  establishing 
the  existence  of  three  new  radio-active  substances 
in  pitch-blende :  radium  associated  with  the  ba- 
rium in  the  mineral,  and  closely  resembling  it  in 
its  chemical  properties ;  polonium  associated  with 
the  bismuth,  and  actinium  with  the  thorium.  They 
succeeded  in  isolating  the  first  of  these  and  deter- 
mined its  combining  weight,  which  was  found  to  be 
225.  Its  spectrum  has  been  discovered  and  exam- 
ined by  Demarcay.  Neither  polonium  nor  actinium 
has  yet  been  isolated,  nor  have  their  spectra 
been  observed.  The  activity  of  polonium  has 
been  found  to  be  fugitive,  dying  away  in  some 
months  after  its  preparation. 

These  radio-active  substances  are  not  confined 
to  rare  minerals.  I  have  lately  found  that  many 
specimens  of  water  from  deep  wells  contain  a 
radio-active  gas,  and  Elster  and  Geitel  have  found 
that  a  similar  gas  is  contained  in  the  soil. 

These  radio-active  substances  may  be  expected 
to  be  of  the  greatest  possible  assistance  in  the  task 
of  investigating  problems  dealing  with  the  nature 
of  the  atom,  and  with  the  changes  that  go  on  in 


142  ELECTRICITY   AND    MATTER 

the  atom  from  time  to  time.  For  the  properties 
possessed  by  these  substances  are  so  marked  as  to 
make  the  detection  of  exceedingly  minute  quanti- 
ties of  them  a  matter  of  comparative  ease.  The 
quantity  of  these  substances  which  can  be  detected 
is  to  the  corresponding  amount  of  the  other  ele- 
ments which  have  to  be  detected  by  the  ordinary 
methods  of  chemical  analysis,  in  the  proportion  of 
a  second  to  thousands  of  years.  Thus,  changes 
which  would  have  to  go  on  for  almost  geological 
epochs  with  the  non-radio-active  substances,  be- 
fore they  became  large  enough  to  be  detected, 
could  with  radio-active  substances  prove  appreci- 
able effects  in  the  course  of  a  few  hours. 

Character  of  the  Radiation 

Rutherford  found  that  the  radiation  from  uran 
ium,  and  it  has  subsequently  been  found  that  the 
same  is  true  for  thorium  and  radium,  is  made  up 
of  three  distinct  types  which  he  calls  the  a,  /5,  and 
y  radiations. 

The  a  radiation  is  very  easily  absorbed,  being 
unable  to  penetrate  more  than  a  few  millimetres 
of  air  at  atmospheric  pressure,  the  ft  radiation  is 
much  more  penetrating,  while  the  y  radiation  is 
the  most  penetrating  of  all.  Investigations  of  the 


RADIO-ACTIVE    SUBSTANCES 

effects  of  magnetic  and  electric  forces  on  these 
three  types  of  radiation  have  shown  that  they  are 
of  entirely  different  characters.  Becquerel  showed 
that  the  fi  rays  were  deflected  by  electric  and  mag- 
netic forces,  the  direction  of  the  deflection  show- 
ing that  the  rays  carried  a  charge  of  negative  elec- 
tricity. He  determined,  using  the  method  described 

in  Chapter  IV,  the  value  of  — ,  the  ratio  of  the 

m 

charge  to  the  mass  of  the  carriers  of  the  negative 
electricity ;  he  found  that  it  was  about  10T,  and  that 
the  velocity  for  some  of  the  rays  was  more  than 
two-thirds  that  of  light.  He  thus  proved  that  the 
/?  rays  consisted  of  corpuscles  travelling  at  prodig- 
ious speeds. 

The  a  rays  are  not  nearly  so  easily  deflected  as 
the  ft  rays,  but  Eutherford  has  recently  shown 
that  they  can  be  deflected,  and  the  direction  of 
deflection  shows  that  they  carry  a,  positive  charge. 
He  finds,  and  his  measurements  have  been  con 

firmed  bv  Des  Coudres.  that  the  ratio  of  —  is  6  X 

m 

103,  and  the  velocity  of  these  particles  is  2  X  109 
centimetres  per  second.  The  value  of  —  shows  that 
the  carriers  of  the  positive  electrification  have 


144  ELECTRICITY    AND    MATTER 

masses  comparable  with  those  of  ordinary  atoms ; 

thus  —  for  hydrogen  is  104  and  for  helium  2.5  X 
m 

103.  The  very  high  velocity  with  which  these  are 
shot  out  involves  an  enormous  expenditure  of  en- 
ergy, a  point  to  which  we  shall  return  later.  One 
of  the  most  interesting  things  about  this  result  is 

that  the  value  of  —  shows  that  the  atoms  shot  off 
m 

are  not  the  atoms  of  radium,  indicating  either  that 
radium  is  a  compound  containing  lighter  elements 
or  else  that  the  atom  of  radium  is  disintegrating 

into  such  elements.     The  value  of  —    for   the   a 

m 

rays  obtained  by  Rutherford  and  Des  Coudres 
suggests  the  existence  of  a  gas  heavier  than  hy- 
drogen but  lighter  than  helium.  The  y  rays,  as 
far  as  we  know,  are  not  deflected  either  by  mag- 
netic or  electric  forces. 

There  is  considerable  resemblance  between  a 
radio-active  substance  and  a  substance  emitting 
secondary  radiation  under  the  influence  of  Ront- 
gen  rays  :  the  secondary  radiation  is  known  to 
contain  radiation  of  the  ft  and  y  types ;  and  as 
part  of  the  radiation  is  exceedingly  easily  absorbed, 
being  unable  to  penetrate  more-  than  a  millimetre 
or  so  of  air  at  atmospheric  pressure,  it  is  possible 


RADIO-ACTIVE    SUBSTANCES  145 

that  closer  investigation  may  show  that  a  rays,  i.e., 
positively  electrified  particles,  are  present  also. 
This  analogy  raises  the  question  as  to  whether 
there  may  not,  in  the  case  of  the  body  struck  by 
the  Rontgen  rays,  be  a  liberation  of  energy 
such  as  we  shall  see  occurs  in  the  case  of  the 
radio-active  substances,  the  energy  emitted  by  the 
radiating  substances  being  greater  than  the  energy 
in  the  Rontgen  rays  falling  upon  it;  this  excess  of 
energy  being  derived  from  changes  taking  place 
in  the  atoms  of  the  body  exposed  to  the  Rontgen 
rays.  This  point  seems  worthy  of  investigation, 
for  it  might  lead  to  a  way  of  doing  by  external 
agency  what  radio-active  bodies  can  do  spontane- 
ously, i.e.,  liberate  the  energy  locked  up  in  the 
atom. 

Emcmation  from  Radio-Active  Substances 

Rutherford  proved  that  thorium  emits  some- 
thing which  is  radio-active  and  which  is  wafted 
about  by  currents  of  air  as  if  it  were  a  gas ;  in 
order  to  avoid  prejudging  the  question  as  to  the 
physical  state  in  which  the  substance  given  off  by 
radium  exists,  Rutherford  called  it  the  "  emana- 
tion." The  emanation  can  pass  through  water  or 
the  strongest  acid  and  can  be  raised  to  tempera- 


146  ELECTRICITY   AND    MATTER 

tures  at  which  platinum  is  incandescent  without 
suffering  any  loss  of  radio-activity.  In  this  inertness 
it  resembles  the  gases  argon  and  helium,  the  latter 
of  which  is  almost  always  found  associated  with 
thorium.  The  radio-activity  of  the  thorium  emana- 
tion is  very  transient,  sinking  to  half  its  value  in 
about  one  minute. 

The  Curies  found  that  radium  also  gives  off 
a  radio-active  emanation  which  is  much  more 
persistent  than  that  given  off  by  thorium,  taking 
about  four  days  to  sink  to  half  its  activity. 

There  seems  every  reason  for  thinking  that 
those  emanations  are  radio-active  matter  in  the 
gaseous  form ;  they  can  be  wafted  from  one  place 
to  another  by  currents  of  air  ;  like  a  gas  they  dif- 
fuse through  a  porous  plug  at  a  rate  which  shows 
that  their  density  is  very  high.  They  diffuse 
gradually  through  air  and  other  gases.  The  coeffi- 
cient of  diffusion  of  the  radium  emanation  through 
air  has  been  measured  by  Rutherford  and  Miss 
Brooks  and  they  concluded  that  the  density  of 
the  emanation  was  about  eighty.  The  emanation 
of  radium  has  been  liquefied  by  Rutherford  and 
Soddy ;  and  I  have,  by  the  kindness  of  Professor 
Dewar,  been  able  to  liquefy  the  radio-active  gas 
found  in  water  from  deep  wells,  which  very 


RADIO-ACTIVE    SUBSTANCES  147 

closely  resembles  the  emanation  and  is  quite 
possibly  identical  with  it.  In  short  the  emana- 
tions seem  to  satisfy  every  test  of  the  gaseous 
state  that  can  be  applied  to  them.  It  is  true 
that  they  are  not  capable  of  detection  by  any 
chemical  tests  of  the  ordinary  type,  nor  can  they 
be  detected  by  spectrum  analysis,  but  this  is  only 
because  they  are  present  in  very  minute  quantities 
— quantities  far  too  small  to  be  detected  even  by 
spectrum  analysis,  a  method  of  detection  which  is 
exceedingly  rough  when  compared  with  the  elec- 
trical methods  which  we  are  able  to  employ  for 
radio-active  substances.  It  is  not,  I  think,  an  ex- 
aggeration to  say  that  it  is  possible  to  detect  with 
certainty  by  the  electrical  method  a  quantity  of  a 
radio-active  substance  less  than  one-hundred-thou- 
sandth part  of  the  least  quantity  which  could  be 
detected  by  spectrum  analysis. 

Each  portion  of  a  salt  of  radium  or  thorium  is 
giving  off  the  emanation,  whether  that  portion  be 
on  the  inside  or  the  outside  of  the  salt;  the 
emanation  coming  from  the  interior  of  a  salt,  how- 
ever, does  not  escape  into  the  air,  but  gets  entangled 
in  the  salt  and  accumulates.  If  such  a  radio- 
active salt  is  dissolved  in  water,  there  is  at  first  a 
great  evolution  of  the  emanation  which  has  been 


148  ELECTRICITY    AND    MATTER 

stored  up  in  the  solid  salt.  The  emanation  can  be 
extracted  from  the  water  either  by  boiling  the 
water  or  bubbling  air  through  it.  The  stored  up 
emanation  can  also  be  driven  off  from  salts  in  the 
solid  state  by  raising  them  to  a  very  high  tem- 
perature. 

Induced  Radio-Activity 

Rutherford  discovered  that  substances  exposed 
to  the  emanation  from  thorium  become  radio-active, 
and  the  Curies  discovered  almost  simultaneously 
that  the  same  property  is  possessed  by  the  emana- 
tion from  radium.  This  phenomenon  is  called  in- 
duced radio-activity.  The  amount  of  induced 
radio-activity  does  not  depend  upon  the  nature  of 
the  substance  on  which  it  is  induced ;  thus,  paper 
becomes  as  radio-active  as  metal  when  placed 
in  contact  with  the  emanations  of  thorium  or 
radium. 

The  induced  radio-activity  is  especially  de- 
veloped on  substances  which  are  negatively  elec- 
trified. Thus,  if  the  emanation  is  contained  in  a 
closed  vessel,  in  which  a  negatively  electrified  wire 
is  placed,  the  induced  radio-activity  is  concentrated 
on  the  negatively  electrified  wire,  and  this  induced 
activity  can  be  detected  on  negatively  electrified 


RADIO-ACTIVE    SUBSTANCES  149 

bodies  when  it  is  too  weak  to  be  detected  on  un- 
electrified  surfaces.  The  fact  that  the  nature  of 
the  induced  radio-activity  does  not  depend  on  the 
substance  in  which  it  is  induced  points  to  its  being 
due  to  a  radio-active  substance  which  is  deposited 
from  the  emanation  on  substances  with  which  it 
comes  in  contact. 

Further  evidence  of  this  is  afforded  by  an  ex- 
periment made  by  Miss  Gates,  in  which  the  in- 
duced radio-activity  on  a  fine  wire  was,  by  raising 
it  to  incandescence,  driven  off  the  wire  and  de- 
posited on  the  surrounding  surfaces.  The  induced 
radio-activity  due  to  the  thorium  emanation  is 
very  different  from  that  due  to  the  radium  emana- 
tion, for  whereas  the  activity  of  the  thorium  ema- 
nation is  so  transient  that  it  drops  to  half  its 
value  in  one  minute,  the  induced  radio-activity 
due  to  it  takes  about  eleven  hours  to  fall  in  the 
same  proportion.  The  emanation  due  to  radium, 
which  is  much  more  lasting  than  the  thorium 
emanation,  taking  about  four  days  instead  of  one 
minute  to  fall  to  half  its  value,  gives  rise  to  a  very 
much  less  durable  induced  radio-activity,  one  fall, 
ing  to  half  its  value  in  about  forty  minutes  instead 
of,  as  in  the  case  of  thorium,  eleven  hours.  The 
emanation  due  to  actinium  is  said  only  to  be  active 


150  ELECTRICITY   AND    MATTER 

for  a  few  seconds,  but  the  induced  radio-activity 
due  to  it  seems  to  be  nearly  as  permanent  as  that 
due  to  radium. 

Separation  of  the  Active  Constituent  from  Thorium 

Rutherford  and  Soddy,  in  a  most  interesting 
and  important  investigation,  have  shown  that  the 
radio-activity  of  thorium  is  due  to  the  passage  of 
the  thorium  into  a  form  which  they  call  ThX, 
which  they  showed  could  be  separated  from  the 
rest  of  the  thorium  by  chemical  means.  When  this 
separation  has  been  effected  the  thorium  left  be- 
hind is  for  a  time  deprived  of  most  of  its  radio-activ- 
ity, which  is  now  to  be  found  in  the  T  h  X.  The 
radio-activity  of  the  thorium  X  slowly  decays  while 
that  of  the  rest  of  the  thorium  increases  until  it 
has  recovered  its  original  activity.  While  this  has 
been  going  on,  the  radio-activity  of  the  T  h  JThas 
vanished.  The  time  taken  for  the  radio-activity 
of  the  T  h  X  to  die  away  to  half  its  original  value 
has  been  shown  by  Rutherford  and  Soddy  to  be 
equal  to  the  time  taken  by  the  thorium  from  which 
the  TTiX  has  been  separated  to  recover  half  its 
original  activity.  All  these  results  support  the 
view  that  the  radio-active  part  of  the  thorium,  the 
thorium  X,  is  continually  being  produced  from  the 


RADIO-ACTIVE    SUBSTANCES 

thorium  itself;  so  that  if  the  activity  of  thorium 
X  were  permanent,  the  radio-activity  of  the  tho- 
rium would  continually  increase.  The  radio-activ. 
ity  of  the  thorium  X,  however,  steadily  dies  away. 
This  prevents  the  unlimited  increase  of  the  radio- 
activity of  the  mixture,  which  will  reach  a  steady 
value  when  the  increase  in  the  radio-activity  due 
to  the  production  of  fresh  T  Ji  X  is  balanced  by 
the  decay  in  the  activity  of  that  already  produced. 
The  question  arises  as  to  what  becomes  of  the 
Th  X  and  the  emanation  when  they  have  lost  their 
radio-activity.  This  dead  TliX,  as  we  may  call 
it,  is  accumulating  all  the  time  in  the  thorium; 
but  inasmuch  as  it  has  lost  its  radio-activity,  we 
have  only  the  ordinary  methods  of  chemical  analy- 
sis to  rely  upon,  and  as  these  are  almost  infinitely 
less  delicate  than  the  tests  we  can  apply  to  radio- 
active substances,  it  might  take  almost  geological 
epochs  to  accumulate  enough  of  the  dead  ThX 
to  make  detection  possible  by  chemical  analysis. 
It  seems  possible  that  a  careful  examination  of  the 
minerals  in  which  thorium  and  radium  occur 
might  yield  important  information.  It  is  remark- 
able that  helium  is  almost  invariably  a  constitu- 
ent of  these  minerals. 

You  will  have  noticed  how  closely,  as  pointed 


ELECTRICITY   AND   MATTER 

out  by  Kutherford  and  Soddy,  the  production  of 
radio-activity  seems  connected  with  changes  tak- 
ing place  in  the  radio-active  substance.  Thus,  to 
take  the  case  of  thorium,  which  is  the  one  on 
which  we  have  the  fullest  information, we  have  first 
the  change  of  thorium  into  thorium  X,  then  the 
change  of  the  thorium  X  into  the  emanation  and 
the  substance  forming  the  a  rays.  The  radio- 
activity of  the  emanation  is  accompanied  by  a  fur- 
ther transformation,  one  of  the  products  being  the 
substance  which  produces  induced  radio-activity. 

On  this  view  the  substance  while  radio-active 
is  continually  being  transformed  from  one  state 
to  another.  These  transformations  may  be  ac- 
companied by  the  liberation  of  sufficient  energy 
to  supply  that  carried  off  by  the  rays  it  emits 
while  radio-active.  The  very  large  amount  of 
energy  emitted  by  radio-active  substances  is  strik- 
ingly shown  by  some  recent  experiments  of  the 
Curies  on  the  salts  of  radium.  They  find  that  those 
salts  give  out  so  much  energy  that  the  absorption 
of  this  by  the  salt  itself  is  sufficent  to  keep  the 
temperature  of  the  salt  permanently  above  that  of 
the  air  by  a  very  appreciable  amount — in  one  of 
their  experiments  as  much  as  1.5°  C.  It  appears 
from  their  measurements  that  a  gram  of  radium 


RADIO-ACTIVE    SUBSTANCES  153 

gives  out  enough  energy  per  hour  to  raise  the 
temperature  of  its  own  weight  of  water  from  the 
freezing  to  the  boiling  point.  This  evolution  of 
energy  goes  on  uninterruptedly  and  apparently 
without  diminution.  If,  however,  the  views  we 
have  just  explained  are  true,  this  energy  arises 
from  the  transformation  of  radium  into  other 
forms  of  matter,  and  its  evolution  must  cease  when 
the  stock  of  radium  is  exhausted ;  unless,  indeed, 
this  stock  is  continually  being  replenished  by  the 
transformation  of  other  chemical  elements  into 
radium. 

We  may  make  a  rough  guess  as  to  the  probable 
duration  of  a  sample  of  radium  by  combining  the 
result  that  a  gram  of  radium  gives  out  100 
calories  per  hour  with  Kutherford's  result  that 
the  a  rays  are  particles  having  masses  comparable 
with  the  mass  of  an  atom  of  hydrogen  projected 
with  a  velocity  of  about  2  X  109  centimetres  per 
second  ;  for  let  us  suppose  that  the  heat  measured 
by  the  Curies  is  due  to  the  bombardment  of  the 
radium  salt  by  these  particles,  and  to  get  a 
superior  limit  to  the  time  the  radium  will  last, 
let  us  make  the  assumption  that  the  whole  of  the 
mass  of  radium  gets  transformed  into  the  a  par- 
ticles (as  a  matter  of  fact  we  know  that  the  emana- 


ELECTRICITY  AND   MATTER 

tion  is  produced  as  well  as  the  a  particles).  Let 
cc  be  the  life  in  hours  of  a  gram  of  radium  ; 
then  since  the  gram  emits  per  hour  100  calories, 
or  4.2  X  109  ergs>  the  amount  of  energy  emitted  by 
the  radium  during  its  life  is  x  X  4.2  X  109  ergs- 
If  -2V  is  the  number  of  a  particles  emitted  in  this 
time,  m  the  mass  of  one  of  them  in  grams,  v 
the  velocity,  then  the  energy  in  the  a  particles  is 
i  Nmv*,  but  this  is  to  be  equal  to  x  X  4.2  X  109 
ergs,  hence  i  Nm  v2  =  x  X  4.2  X  109 ;  but  if  the 
gram  of  radium  is  converted  into  the  a  particles, 
Nm  =  1,  and  by  Rutherford's  experiments  v  =  2 

4  X  1018        109 
X  109,   hence   we   have   ^:zi4>2  x  10>     r  2! 

hours,  or  about  50,000  years. 

From  this  estimate  we  should  expect  the  life 
of  a  piece  of  radium  to  be  of  the  order  of  50,000 
years.  This  result  shows  that  we  could  not 
expect  to  detect  any  measurable  changes  in  the 
space  of  a  few  months.  In  the  course  of  its  life 
the  gram  of  radium  will  have  given  out  about 
5  X  1010  calories,  a  result  which  shows  that  if  this 
energy  is  derived  from  transformations  in  the 
state  of  the  radium,  the  energy  developed  in  these 
transformations  must  be  on  a  very  much  greater 
scale  than  that  developed  in  any  known  chemical 


RADIO-ACTIVE    SUBSTANCES  155 

reactions.  On  the  view  we  have  taken  the  differ- 
ence between  the  case  of  radium  and  that  of  or- 
dinary chemical  reactions  is  that  in  the  latter  the 
changes  are  molecular,  while  in  the  case  of  ra- 
dium the  changes  are  atomic,  being  of  the  nature 
of  a  decomposition  of  the  elements.  The  example 
given  on  page  (111)  shows  how  large  an  amount 
of  energy  may  be  stored  up  in  the  atom  if  we  re- 
gard it  as  built  up  of  a  number  of  corpuscles,  i/ 
We  may,  I  think,  get  some  light  on  the  processes 
going  on  in  radium  by  considering  the  behavior 
of  a  model  atom  of  the  kind  described  on  page 
124,  and  which  may  be  typified  by  the  case  of 
the  corpuscles  which  when  rotating  with  a  high 
velocity  are  stable  when  arranged  in  a  certain 
way,  which  arrangement  becomes  unstable  when 
the  energy  sinks  below  a  certain  value  and  is 
succeeded  by  another  configuration.  A  top  spin- 
ning about  a  vertical  axis  is  another  model  of  the 
same  type.  This  is  stable  when  in  a  vertical 
position  if  the  kinetic  energy  due  to  its  rotation 
exceeds  a  certain  value.  If  this  energy  were 
gradually  to  decrease,  then,  when  it  reached  the 
critical  value,  the  top  would  become  unstable  and 
would  fall  down,  and  in  so  doing  would  give  a 
considerable  amount  of  kinetic  energy. 


156  ELECTRICITY   AND   MATTER 

Let  us  follow,  then,  the  behavior  of  an  atom  of 
this  type,  i.e.,  one  which  is  stable  in  one  configura- 
tion of  steady  motion  when  the  kinetic  energy  of 
the  corpuscles  exceeds  a  certain  value,  but  be- 
comes unstable  and  passes  into  a  different  config- 
uration when  the  kinetic  energy  sinks  below  that 
value.  Suppose  now  that  the  atom  starts  with  an 
amount  of  kinetic  energy  well  above  the  critical 
value,  the  kinetic  energy  will  decrease  in  conse- 
quence of  the  radiation  from  the  rapidly  moving 
corpuscles;  but  as  long  as  the  motion  remains 
steady  the  rate  of  decrease  will  be  exceedingly 
slow,  and  it  may  be  thousands  of  years  before  the 
energy  approaches  the  critical  value.  When  it  gets 
close  to  this  value,  the  motion  will  be  very  easily 
disturbed  and  there  will  probably  be  considerable 
departure  from  the  configuration  for  steady  motion 
accompanied  by  a  great  increase  in  the  rate  at 
which  kinetic  energy  is  loss  by  radiation.  The  atom 
now  emits  a  much  greater  number  of  rays  and  the 
kinetic  energy  rapidly  approaches  the  critical 
value ;  when  it  reaches  this  value  the  crash  comes, 
the  original  configuration  is  broken  up,  there  is  a 
great  decrease  in  the  potential  energy  of  the  sys- 
tem accompanied  by  an  equal  increase  in  the 
kinetic  energy  of  the  corpuscles.  The  increase  in 


RADIO-ACTIVE    SUBSTANCES  157 

the  velocity  of  the  corpuscles  may  cause  the  dis- 
ruption of  the  atom  into  two  or  more  systems,  cor- 
responding to  the  emission  of  the  a  rays  and 
the  emanation. 

If  the  emanation  is  an  atom  of  the  same  type 
as  the  original  atom,  i.e.,  one  whose  configuration 
for  steady  motion  depends  on  its  kinetic  energy, 
the  process  is  repeated  for  the  emanation,  but  in  a 
very  much  shorter  time,  and  is  repeated  again  for 
the  various  radio-active  substances,  such  as  the 
induced  radio-active  substance  formed  out  of  the 
emanation. 

We  have  regarded  the  energy  emitted  by 
radium  and  other  radio-active  substances  as  de- 
rived from  an  internal  source,  i.e.,  changes  in  the 
constitution  of  the  atom ;  as  changes  of  this  kind 
have  not  hitherto  been  recognized,  it  is  desirable 
to  discuss  the  question  of  other  possible  sources 
of  this  energy.  One  source  which  at  once  sug- 
gests itself  is  external  to  the  radium.  We  might 
suppose  that  the  radium  obtained  its  energy  by 
absorbing  some  form  of  radiation  which  is  passing 
through  all  bodies  on  the  surface  of  the  earth, 
but  which  is  not  absorbed  to  any  extent  by  any 
but  those  which  are  radio-active.  This  radiation 
must  be  of  a  very  penetrating  character,  for  radium 


158  ELECTRICITY    AND    MATTER 

retains  its  activity  when  surrounded  by  thick  lead 
or  when  placed  in  a  deep  cellar.  We  are  familiar 
with  forms  of  Rontgen  rays,  and  of  rays  given 
out  by  radium  itself,  which  can  produce  appreci- 
able effects  after  passing  through  several  inches  of 
lead,  so  that  the  idea  of  the  existence  of  very  pene- 
trating radiation  does  not  seem  so  improbable  as  it 
would  have  done  a  few  years  ago.  It  is  interest- 
ing to  remember  that  very  penetrating  radiation 
was  introduced  by  Le  Sage  more  than  a  century 
ago  to  explain  gravitation.  Le  Sage  supposed 
that  the  universe  was  thronged  with  exceedingly 
small  particles  moving  with  very  high  velocities. 
He  called  these  ultra-mundane  corpuscles  and  as- 
sumed that  they  were  so  penetrating  that  they 
could  pass  through  masses  as  large  as  the  sun  or 
the  planets  without  suffering  more  than  a  very 
slight  absorption.  They  were,  however,  absorbed 
to  a  slight  extent  and  gave  up  to  the  bodies 
through  which  they  passed  a  small  fraction  of 
their  momentum.  If  the  direction  of  the  ultra- 
mundane corpuscles  passing  through  a  body  were 
uniformly  distributed,  the  momentum  communi- 
cated by  them  to  the  body  would  not  tend  to  move 
it  in  one  direction  rather  than  another,  so  that 
a  body  A  alone  in  the  universe  and  exposed  to 


RADIO-ACTIVE    SUBSTANCES  ^59 

bombardment  by  Le  Sage's  corpuscles  would  re- 
main at  rest ;  if,  however,  there  is  a  second  body 
B  in  the  neighborhood  of  A,  B  will  shield  off 
from  A  some  of  the  corpuscles  moving  in  the 
direction  B  A  ;  thus,  A  will  not  receive  as  much 
momentum  in  this  direction  as  it  did  when  it  was 
alone  in  the  field,  but  in  the  latter  case  it  only  re- 
ceived enough  momentum  in  this  direction  to  keep 
it  in  equilibrium ;  hence,  when  B  is  present,  the 
momentum  in  the  opposite  direction  will  get  the 
upper  hand  so  that  A  will  move  in  the  direction, 
A  B,  i.e.,  will  be  attracted  to  B.  Maxwell  pointed 
out  that  this  transference  of  momentum  from  Le 
Sage's  corpuscles  to  the  body  through  which  they 
were  passing  involved  the  loss  of  kinetic  energy 
by  the  corpuscles  ;  and  that  if  the  loss  of  momen- 
tum were  sufficient  to  account  for  gravitation, 
the  kinetic  energy  lost  by  the  ultra-mundane  cor- 
puscles would  be  sufficient,  if  converted  into  heat, 
to  keep  the  gravitating  body  white  hot.  The 
fact  that  all  bodies  are  not  white  hot  was  urged 
by  Maxwell  as  an  argument  against  Le  Sage's 
theory.  It  is  not  necessary,  however,  to  suppose 
that  the  energy  of  the  corpuscles  is  transformed 
into  heat ;  we  might  imagine  it  transformed  into  a 
very  penetrating  radiation  which  might  escape 


160  ELECTRICITY   AND   MATTER 

from  the  gravitating  body.  A  simple  calculation 
will  show  that  the  amount  of  kinetic  energy 
transformed  per  second  in  each  gram  of  the 
gravitating  body  must  be  enormously  greater  than 
that  given  out  in  the  same  time  by  one  gram  of 
radium. 

We  have  seen  in  the  first  chapter  that  waves 
of  electric  and  magnetic  force  possess  momentum 
in  their  direction  of  propagation;  we  might  there- 
fore replace  Le  Sage's  corpuscles  by  very  pene- 
trating Rontgen  rays.  Those,  if  absorbed,  would 
give  up  momentum  to  the  bodies  through  which 
they  pass,  and  similar  consideration  to  those 
given  by  Le  Sage  would  show  that  two  bodies 
would  attract  each  other  inversely  as  the  square 
of  the  distance  between  them.  If  the  absorption 
of  these  waves  per  unit  volume  depended  only 
upon,  and  was  proportional  to,  the  density,  the 
attraction  between  the  bodies  would  be  directly 
proportional  to  the  product  of  their  masses.  It 
ought  to  be  mentioned  that  on  this  view  any 
changes  in  gravitation  would  be  propagated  with 
the  velocity  of  light;  whereas,  astronomers  be- 
lieve they  have  established  that  it  travels  with  a 
very  much  greater  velocity. 

As  in  the  case  of  Le  Sage's  corpuscles,  the  loss 


RADIO-ACTIVE    SUBSTANCES  ifa 

of  momentum  by  the  Rontgen  rays  would  be  ac- 
companied by  a  loss  of  energy;  for  each  unit  of 
momentum  lost  v  units  of  energy  would  be  lost,  v 
being  the  velocity  of  light.  If  this  energy  were 
transformed  into  that  of  rays  of  the  same  type  as 
the  incident  rays,  a  little  reflection  will  show  that 
he  absorption  of  the  rays  would  not  produce 
gravitational  attraction.  To  get  such  attraction 
the  transformed  rays  must  be  of  a  more  pene- 
trating type  than  the  original  rays.  Again,  as 
in  the  case  of  Le  Sage's  corpuscles,  the  absorp- 
tion of  energy  from  these  rays,  if  they  are  the 
cause  of  gravitation,  must  be  enormous — so  great 
that  the  energy  emitted  by  radium  would  be  but 
an  exceedingly  small  fraction  of  the  energy  being 
transformed  within  it.  From  these  considerations 
I  think  that  the  magnitude  of  the  energy  radiated 
from  radium  is  not  a  valid  argument  against  the 
energy  being  derived  from  radiation.  The  reason 
which  induces  me  to  think  that  the  source  of  the 
energy  is  in  the  atom  of  radium  itself  and  not  ex- 
ternal to  it  is  that  the  radio-activity  of  substances 
is,  in  all  cases  in  which  we  have  been  able  to  local- 
ize it,  a  transient  property.  No  substance  goes  on 
being  radio-active  for  very  long.  It  may  be  asked 
how  can  this  statement  be  reconciled  with  the  fact 


162  ELECTRICITY    AND   MATTER 

that  thorium  and  radium  keep  up  their  activity 
without  any  appreciable  falling  off  with  time. 
The  answer  to  this  is  that,  as  Rutherford  and 
Soddy  have  shown  in  the  case  of  thorium,  it  is 
only  an  exceedingly  small  fraction  of  the  mass 
which  is  at  any  one  time  radio-active,  and  that  this 
radio-active  portion  loses  its  activity  in  a  few 
hours,  and  has  to  be  replaced  by  a  fresh  supply 
from  the  non-radio-active  thorium.  Take  any  of 
the  radio-active  substances  we  have  described,  the 
ThXj  the  emanations  from  thorium  or  radium, 
the  substance  which  produces  induced  radio- 
activity, all  these  are  active  for  at  the  most  a  few 
days  and  then  lose  this  property.  This  is  what 
we  should  expect  on  the  view  that  the  source  of 
the  radio-activity  is  a  change  in  the  atom ;  it  is 
not  what  we  should  expect  if  the  source  were  ex- 
ternal radiation. 


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